Letter Agreement by and between Unifi, Inc. and Albert P. Carey, effective as of June 29, 2020

Exhibit 10.2

Mr. Albert P. Carey

7201 West Friendly Avenue Greensboro, North Carolina 27410

Dear Al:

On behalf of the Board of Directors (the “Board”) of Unifi, Inc. (the “Company”), we are pleased to continue your employment as Executive Chairman of the Company on the following terms:

1.Position. The Company shall employ you as Executive Chairman of the Board and you agree to provide the services described in Section 2 hereof. Upon your execution and signature, your employment under this letter is effective as of June 29, 2020 (the “Employment Date”), and this letter replaces any prior agreements between you and the Company.

2.Duties. You shall continue to report to the Board and your duties shall be to: (a) provide leadership to the Board and the Company’s executive management; (b) act as the primary spokesperson for the Board; (c) act as an adviser and confidant to the Chief Executive Officer of the Company;

(d) assist with developing the Company’s corporate strategy; (e) in conjunction with management, lead the Company in its relationships with shareholders and business and customer relationships; (f) lead efforts regarding management succession; and (g) have such other duties as the Board may reasonably determine. The Company’s principal executive officer shall remain the Chief Executive Officer of the Company.

3.Term; Termination. Your employment shall continue until the Company’s annual shareholders’ meeting in 2021 and shall be extended by mutual agreement of the Board and you for successive periods thereafter between each of the Company’s annual shareholders meeting (the period of actual employment, the “Term”). The Term, and your employment hereunder, may be terminated at any time: (a) by you for any or no reason, on 30 days’ prior written notice to the Company (which the Company may, in its sole discretion, make effective as a resignation earlier than the termination date provided in such notice), (b) by the Company, at any time with or without cause by written notice to you, at the election of the Board, and (c) by the Company, at any time with or without cause by written notice to you, due to your failure to be re-elected as a member of the Board by the Company’s shareholders. If either you or the Company provide notice of termination pursuant to either the foregoing clause (a) or clause (b), by signing this letter agreement you hereby offer your resignation as a member of the Board effective concurrent with the termination of the Term, which resignation may or may not be accepted by the Board in its sole discretion.

4.Base Salary. Your base salary shall be $700,000 per fiscal year, payable in accordance with the Company’s regular payroll practices. Compensation is reviewed annually by the Compensation Committee of the Board, provided that your base salary and equity compensation will not be reduced. The Company shall deduct and withhold from any amounts payable under this letter agreement such federal, state, local or other taxes to the extent required to be withheld pursuant to applicable law.

5.Equity Compensation.  You will receive an award consisting of a combination of restricted stock units (“RSUs”) and incentive stock options (“ISOs”) annually, the combination having an aggregate grant date value equal to $700,000. Each such award shall be consistent with the Company’s practices for

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other management equity awards and will be subject to the terms of the related RSU and ISO agreements and the terms and conditions of the Company’s Amended and Restated 2013 Incentive Compensation Plan (as such plan may be amended, modified, or replaced). This award will be in lieu of any compensation payable to you as a member of the Board. Nothing herein shall affect any outstanding equity agreements between you and the Company prior to the execution of this letter agreement.

6.Reimbursement of Expenses. The Company shall promptly reimburse you for all reasonable and necessary expenses actually incurred by you directly in connection with the business and affairs of the Company and the performance of your duties hereunder, in each case subject to appropriate substantiation and itemization of such expenses and fees in accordance with the guidelines and limitations established by the Company from time to time.

7.Nondisclosure of Confidential Information; Protected Disclosures. You and we agree that your duties under the terms of this letter agreement would result in your acquiring confidential information concerning the Company and its affiliates. You shall not, except in the course of the good faith performance of your duties hereunder or as required by applicable law, without limitation in time or until such information shall have become public other than by your unauthorized disclosure, disclose to others or use, whether directly or indirectly, any Confidential Information (as hereinafter defined) regarding the Company. For purposes of this letter agreement, “Confidential Information” shall mean information about the Company or its clients or customers that was learned by you in the course of your employment by the Company, including (without limitation) any proprietary knowledge, trade secrets, data, formulae, information and client and customer lists and all papers, resumes, and records (including computer records) of the documents containing such Confidential Information, but excludes information

(i) which is in the public domain through no unauthorized act or omission of you; or (ii) which becomes available to you on a non-confidential basis from a source other than the Company without breach of such source’s confidentiality or non-disclosure obligations to the Company. You agree to deliver or return to the Company, at the Company’s request at any time or upon termination or expiration of your employment or as soon thereafter as possible, (i) all documents, computer tapes and disks, records, lists, data, drawings, prints, notes and written information (and all copies thereof) furnished by the Company or prepared by you during the term of your employment by the Company and (ii) all notebooks and other data relating to research or experiments or other work conducted by you in the scope of such employment. Upon the date of termination of your employment hereunder, you shall, as soon as possible but no later than two (2) days after the date of termination, surrender to the Company all Confidential Information in Executive’s possession and return to the Company all Company property in your possession or control, including but not limited to, all paper records and documents, computer disks and access cards and keys to any Company facilities. This Section 7 shall survive the termination of this letter agreement. Pursuant to the Defend Trade Secrets Act of 2016 (8 U.S.C. § 1833(b)), you will not be held criminally or civilly liable under any federal or state trade secret law for the disclosure of a trade secret of the Company that

(i) is made (A) in confidence to a federal, state, or local government official, either directly or indirectly, or to an attorney and (B) solely for the purpose of reporting or investigating a suspected violation of law; or (ii) is made in a complaint or other document that is filed under seal in a lawsuit or other proceeding. If you file a lawsuit for retaliation by the Company for reporting a suspected violation of law, you may disclose the trade secret to your attorney and use the trade secret information in the court proceeding, if you (i) file any document containing the trade secret under seal, and (ii) do not disclose the trade secret, except pursuant to court order. Nothing in this letter agreement, is intended to conflict with 18 U.S.C. § 1833(b) or create liability for disclosures of trade secrets that are expressly allowed by such section. Notwithstanding any provision in any agreement between the Company and you, you may disclose any confidential or non-public information (i) to report possible violations of federal law or regulation to any governmental agency or entity, including but not limited to the Department of Justice, the Securities and

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Exchange Commission, the United States Congress and any agency Inspector General, or make other disclosures that are protected under the whistleblower provisions of federal law or regulation or (ii) as required by law or order by a court; provided, however, you agree to notify the Company in advance if you are required to provide information or testimony in connection with any action brought by a non- governmental or non-regulatory person or entity.

8.Miscellaneous. All notices hereunder, to be effective, shall be in writing and shall be deemed effective when delivered by hand or mailed by certified mail, postage and fees prepaid, or nationally recognized overnight express mail service, (a) if to you, in person or at the address last on file with the Company as your home address for payroll purposes and (b) if to the Company, at its corporate headquarters. This letter agreement constitutes the entire agreement and understanding between the Company and you with regard to the subject matter hereof and supersedes all prior understandings and agreements with respect to the subject matter hereof, whether written or oral. This letter agreement may not be amended, supplemented or modified except by an instrument in writing signed on behalf of the Company and you. Any term or condition of this letter agreement may be waived at any time by the party that is entitled to the benefit thereof, but no such waiver shall be effective, unless set forth in a written instrument duly executed by or on behalf of the party waiving such term or condition. No waiver by any party of any term or condition of this letter agreement, in any one or more instances, shall be deemed to be or construed as a waiver of the same or any other term or condition of this letter agreement on any future occasion. This letter agreement shall be governed by and interpreted and enforced in accordance with the laws of the State of North Carolina, without giving effect to any choice of law or conflict of laws rules or provisions (whether of the State of North Carolina or any other jurisdiction) that would cause the application of the laws of any jurisdiction other than the State of North Carolina. This letter agreement may be executed in counterparts, and either party hereto may execute any such counterpart, each of which when executed and delivered shall be deemed to be an original and all of which counterparts taken together shall constitute but one and the same instrument. The parties agree that the delivery of this letter agreement may be effected by means of an exchange of facsimile or electronically transmitted signatures.

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If the above terms and conditions are satisfactory to you, please sign both copies of this letter indicating your acceptance and return them to me. An original executed copy will be returned to you.

Yours sincerely, UNIFI, INC.

   /s/ ARCHIBALD COX, JR.

Archibald Cox, Jr.

Lead Independent Director

I hereby acknowledge my receipt and acceptance of the terms and conditions of this offer of employment.

  /s/ ALBERT P. CAREY

Albert P. Carey

Date: November 2, 2020