Exhibit 10.1

TERMINATION OF FORWARD SHARE PURCHASE AGREEMENT

THIS TERMINATION OF FORWARD SHARE PURCHASE AGREEMENT (this “Agreement”) is made as of February 22, 2022 (the “Effective Date”), by and among BigBear.ai Holdings, Inc., a Delaware corporation (as successor-in-interest to GigCapital4, Inc., a Delaware corporation) (“BigBear”), Glazer Capital, LLC, a Delaware limited liability company (“Glazer”), and Meteora Capital, LLC, a Delaware limited liability company (“Meteora”), on behalf of itself and its affiliated investment funds. Each of Big Bear, Glazer and Meteora is individually referred to herein as a “Party”and together, the “Parties”).

WHEREAS, BigBear, Glazer and Meteora are parties to that certain Forward Share Purchase Agreement, dated October 14, 2021 (as amended, the “FSPA”); and

WHEREAS, pursuant to Section 6(a) of the FSPA, the Parties desire to terminate the FSPA on the terms and conditions set forth herein.

NOW, THEREFORE, for good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the Parties hereby agree as follows:

1.    Purchase and Sale of Purchased Shares. Notwithstanding anything to the contrary set forth in the FSPA, in full, final and complete satisfaction of each Party’s rights and obligations under the FSPA, upon the execution and delivery of this Agreement, BigBear shall purchase from each Investor, and each Investor shall sell to BigBear, the number of Shares set forth opposite such Investor’s name on Exhibit A attached hereto (with respect to a particular Investor, the “Purchased Shares”), at a price per Share equal to $10.125, for the aggregate purchase price set forth opposite such Investor’s name on Exhibit A attached hereto (with respect to a particular Investor, the “Purchase Price”). Concurrently with the execution of this Agreement (a) each Investor shall deliver, or cause to be delivered, such Investor’s Purchased Shares free and clear of all liens and encumbrances to the Escrow Agent, and (b) the Parties shall deliver, or cause to be delivered, duly executed instructions in the form attached hereto as Exhibit B (the “Joint Release Instructions”) instructing the Escrow Agent (i) to pay to each Investor, in exchange for such Investor’s Purchased Shares, an amount equal to such Investor’s Purchase Price, (ii) to pay to BigBear the remainder of the funds remaining in the Escrow Account after all of the payments to the Investors contemplated in clause (i) above, which payments, in each case of clause (i) and (ii), shall be paid by wire transfer of immediately available funds from the Escrow Account for use by the recipient thereof (or its designee) without restriction, and (iii) to promptly deliver each Investor’s Purchased Shares to BigBear by DWAC.

2.    Representations and Warranties of the Investors. As a material inducement to BigBear to enter into the transactions contemplated by this Agreement, each Principal Investor represents and warrants to BigBear as of the date hereof that:

(a)    Such Principal Investor is duly organized, validly existing and in good standing under the laws of the jurisdiction of its formation and has all requisite power and authority to carry on its business as presently conducted and as proposed to be conducted.

(b)    Such Principal Investor has full power and authority to enter into this Agreement. This Agreement, when executed and delivered by such Principal Investor will constitute the valid and legally binding obligation of such Principal Investor enforceable against it in accordance with its terms, except as limited by the Enforceability Exceptions.

(c)    No consent, approval, order or authorization of, or registration, qualification, designation, declaration or filing with, any federal, state or local governmental authority is required on the part of such Principal Investor (or any of its affiliated Investors) in connection with the consummation of the transactions contemplated by this Agreement, other than disclosure reports regarding such transactions that such Principal Investor (or any of its affiliated Investors) is required to file in accordance with the terms of the Exchange Act.

(d)    The execution, delivery and performance by such Principal Investor of this Agreement and the consummation by such Principal Investor (and each of its affiliated Investors) of the transactions contemplated hereby will not result in any violation or default (i) of any provisions of its organizational documents, (ii) of any instrument, judgment, order, writ or decree to which it is a party or by which it is bound, (iii) under any note, indenture or mortgage to which it is a party or by which it is bound, (iv) under any lease, agreement, contract or purchase order to which it is a party or by which it is bound, or (v) of any provision of federal or state statute, rule or regulation applicable to it, in each case (other than clause (i)), which would have a material adverse effect on such Investor or its ability to consummate the transactions contemplated hereby.

(e)    Such Principal Investor (or each of its affiliated Investors, as applicable) is the record and beneficial owner of all of such Principal Investor’s (or such Investors, as applicable) Purchased Shares set forth on Exhibit A attached hereto and has good, valid and marketable title to such Purchased Shares, free and clear of all liens and encumbrances, other than those existing under applicable securities laws.

3.    Representations and Warranties of BigBear. As a material inducement to each Principal Investor to enter into the transactions contemplated by this Agreement, BigBear represents and warrants to each Principal Investor as of the date hereof that:

(a)    BigBear is a corporation duly incorporated, validly existing and in good standing as a corporation under the laws of the State of Delaware and has all requisite corporate power and authority to carry on its business as presently conducted and as proposed to be conducted.

(b)    All corporate action required to be taken by BigBear’s Board of Directors in order to authorize BigBear to enter into this Agreement has been taken. This Agreement, when executed and delivered by BigBear, shall constitute the valid and legally binding obligation of BigBear, enforceable against BigBear in accordance with its term, subject to the effect of the Enforceability Exceptions.

(c)    The execution, delivery and performance by BigBear of this Agreement and the consummation by BigBear of the transactions contemplated hereby will not result in

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any violation or default (i) of any provisions of its organizational documents, (ii) of any instrument, judgment, order, writ or decree to which it is a party or by which it is bound, (iii) under any note, indenture or mortgage to which it is a party or by which it is bound, (iv) under any lease, agreement, contract or purchase order to which it is a party or by which it is bound, or (v) of any provision of federal or state statute, rule or regulation applicable to it, in each case (other than clause (i)), which would have a material adverse effect on BigBear or its ability to consummate the transactions contemplated hereby.

4.    Miscellaneous.

(a)    Capitalized Terms. All capitalized terms used in this Agreement and not otherwise defined herein shall have the meanings ascribed to such terms in the FSPA.

(b)    Survival of Representations and Warranties. All of the representations and warranties contained herein shall survive the execution and delivery of this Agreement.

(c)    Entire Agreement. This Agreement, together with any documents, instruments and writings that are delivered pursuant hereto or referenced herein, constitute the entire agreement and understanding of the Parties in respect of its subject matter and supersedes all prior understandings, agreements, or representations by or among the Parties, written or oral, to the extent they relate in any way to the subject matter hereof or to the transactions contemplated hereby.

(d)    Successors. All of the terms, agreements, covenants, representations, warranties, and conditions of this Agreement are binding upon, and inure to the benefit of and are enforceable by, the Parties and their respective successors. Nothing in this Agreement, express or implied, is intended to confer upon any party other than the Parties or their respective successors and assigns any rights, remedies, obligations or liabilities under or by reason of this Agreement, except as expressly provided in this Agreement.

(e)    Assignments. Except as otherwise specifically provided herein, no Party may assign either this Agreement or any of its rights, interests, or obligations hereunder without the prior written approval of the each of the other Parties.

(f)    Counterparts. This Agreement may be executed in two or more counterparts, each of which will be deemed an original but all of which together will constitute one and the same instrument. Signatures sent by facsimile transmission or in PDF format shall be deemed to be originals for all purposes of this Agreement.

(g)    Headings. The section headings contained in this Agreement are inserted for convenience only and will not affect in any way the meaning or interpretation of this Agreement.

(h)    Governing Law; Jurisdiction. This Agreement, the entire relationship of the Parties, and any litigation among the Parties (whether grounded in contract, tort, statute, law or equity) shall be governed by, construed in accordance with, and interpreted pursuant to the laws of the State of Delaware, without giving effect to its choice of laws or conflict of law provision or rule (whether of the State of Delaware or any other jurisdiction) that

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would cause the application of the laws of any jurisdiction other than the State of Delaware. Any dispute arising from or relating to the relative rights of the parties hereto and all other questions concerning the construction, validity and interpretation of this Agreement, shall be brought exclusively in the Court of Chancery of the State of Delaware (the “Court of Chancery”) or, to the extent the Court of Chancery does not have subject matter jurisdiction, the United States District Court for the District of Delaware and the appellate courts having jurisdiction of appeals in such courts (the “Delaware Federal Court”) or, to the extent neither the Court of Chancery nor the Delaware Federal Court has subject matter jurisdiction, the Superior Court of the State of Delaware (the “Chosen Courts”), and, solely with respect to any such action (i) irrevocably submits to the exclusive jurisdiction of the Chosen Courts, (ii) waives any objection to laying venue in any such action in the Chosen Courts, and (iii) waives any objection that the Chosen Courts are an inconvenient forum or do not have jurisdiction over any party hereto.

(i)    MUTUAL WAIVER OF JURY TRIAL. EACH PARTY TO THIS AGREEMENT HEREBY WAIVES ALL RIGHTS TO TRIAL BY JURY IN ANY ACTION, SUIT, OR PROCEEDING BROUGHT TO RESOLVE ANY DISPUTE BETWEEN OR AMONG ANY OF THE PARTIES HERETO, WHETHER ARISING IN CONTRACT, TORT, OR OTHERWISE, ARISING OUT OF, CONNECTED WITH, RELATED OR INCIDENTAL TO THIS AGREEMENT AND/OR THE TRANSACTIONS CONTEMPLATED HEREBY.

(j)    Amendments. This Agreement may not be amended, modified or waived as to any particular provision, except with the prior written consent of all Parties.

(k)    Severability. The provisions of this Agreement will be deemed severable and the invalidity or unenforceability of any provision will not affect the validity or enforceability of the other provisions hereof; provided that if any provision of this Agreement, as applied to any Party or to any circumstance, is adjudged by a governmental authority, arbitrator, or mediator not to be enforceable in accordance with its terms, the Parties agree that the governmental authority, arbitrator, or mediator making such determination will have the power to modify the provision in a manner consistent with its objectives such that it is enforceable, and/or to delete specific words or phrases, and in its reduced form, such provision will then be enforceable and will be enforced.

(l)    Construction. The Parties have participated jointly in the negotiation and drafting of this Agreement. If an ambiguity or question of intent or interpretation arises, this Agreement will be construed as if drafted jointly by the Parties and no presumption or burden of proof will arise favoring or disfavoring any Party because of the authorship of any provision of this Agreement. For purposes of this Agreement, “Business Day” means any day other than Saturday, Sunday, or a day on which commercial banks in New York are obligated by any applicable law to close. Any reference to any federal, state, local, or foreign law will be deemed also to refer to law as amended and all rules and regulations promulgated thereunder, unless the context requires otherwise. The words “include,” “includes,” and “including” will be deemed to be followed by “without limitation.” Pronouns in masculine, feminine, and neuter genders will be construed to include any other gender, and words in the singular form will be construed to include the plural and vice

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versa, unless the context otherwise requires. The words “this Agreement,” “herein,” “hereof,” “hereby,” “hereunder,” and words of similar import refer to this Agreement as a whole and not to any particular subdivision unless expressly so limited. The Parties intend that each representation, warranty, and covenant contained herein will have independent significance. If a Party has breached any representation, warranty, or covenant contained herein in any respect, the fact that there exists another representation, warranty or covenant relating to the same subject matter (regardless of the relative levels of specificity) which such party has not breached will not detract from or mitigate the fact that such party is in breach of the first representation, warranty, or covenant.

(m)    Waiver. No waiver by a Party of any default, misrepresentation, or breach of warranty or covenant hereunder, whether intentional or not, may be deemed to extend to any prior or subsequent default, misrepresentation, or breach of warranty or covenant hereunder or affect in any way any rights arising because of any prior or subsequent occurrence.

(n)    Specific Performance. Each Party agrees that irreparable damage may occur in the event any provision of this Agreement was not performed by any other Party in accordance with the terms hereof and that the other Parties shall be entitled to seek specific performance of the terms hereof, in addition to any other remedy at law or equity.

(o)    Further Assurances. In the event that at any time after the execution of this Agreement any further action is necessary or desirable to carry out or evidence the purposes of this Agreement, each of the Parties will take (and, in the case of the Principal Investors, will cause their respective affiliated Investors to take) such further action (including the execution and delivery of such further instruments and documents) as any other Party reasonably may request.

(p)    Security Interests. Each Principal Investor, on behalf of itself and its affiliated Investors, authorizes BigBear and its designees to file on behalf of such Investor (at BigBear’s sole cost and expense) all terminations, releases and other documents reasonably required to release and terminate all liens and security interests of such Investor in any of the Purchased Shares, the Escrow Account or the funds therein, in each case, arising under or relating to the FSPA or the Escrow Agreement; provided that no such release or termination shall impact such Investor’s right to receive such Investor’s Purchase Price in accordance with Section 1.

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IN WITNESS WHEREOF, the undersigned have executed this Agreement as of the date first set forth above.

Signature Page to Termination of Forward Share Purchase Agreement