Supplemental Indenture No. 2, dated as of April 3, 2018, by and among Stone Energy Corporation, Stone Energy Offshore, L.L.C. and The Bank of New York Mellon Trust Company, N.A., as trustee and collateral agent

Exhibit 10.2

Execution Version

SUPPLEMENTAL INDENTURE NO. 2

SUPPLEMENTAL INDENTURE NO. 2, dated as of April 3, 2018 (this “Supplemental Indenture”), by and between Stone Energy Corporation, a Delaware corporation (the “Issuer”), Stone Energy Offshore, L.L.C., as subsidiary guarantor (the “Subsidiary Guarantor”), and The Bank of New York Mellon Trust Company, N.A., as trustee (in such capacity, the “Trustee”) and collateral agent (in such capacity, the “Collateral Agent”).

W I T N E S S E T H

WHEREAS, the Issuer, the Subsidiary Guarantor, the Trustee and the Collateral Agent are party to that certain Indenture, dated as of February 28, 2017 (as supplemented by that certain Supplemental Indenture No. 1, dated as of April 3, 2018, the “Indenture”), providing for the issuance of the Issuer’s 7.500% Senior Secured Notes due 2022 (the “Notes”);

WHEREAS, Section 1002 of the Indenture provides, inter alia, that the Issuer, the Subsidiary Guarantor, the Trustee and the Collateral Agent may amend the Indenture, the Notes and the other Note Documents to release all or substantially all of the Collateral from the Liens securing the Notes with the consent of the Holders of at least 66 2/3% in principal amount of the Outstanding Notes (the “Collateral Release Requisite Consents”);

WHEREAS, Talos Production LLC, a Delaware limited liability company (“Talos Production”) and Talos Production Finance Inc., a Delaware corporation (“Talos Finance” and, together with Talos Production, the “Talos Issuers”), have distributed an Offer to Exchange and Consent Solicitation Statement, dated March 20, 2018 (the “Statement”), and an accompanying Consent and Letter of Transmittal to the holders of the Notes in connection with the offer to exchange the outstanding Notes and the concurrent solicitation (the “Consent Solicitation”) of consents by the Holders of the Notes embodied in and evidenced by instruments signed by Holders (or agents thereof duly appointed in writing) by electronic transmission transmitted through the facilities of the Depository (the “Consents”) to certain proposed amendments to the Indenture as further described in the Statement (the “Proposed Amendments”);

WHEREAS, the aggregate principal amount of the Outstanding Notes (such term excluding Notes owned by controlling persons specified in the definition thereof in the Indenture for purposes of determining whether Holders of the requisite principal amount of Notes have given any consent as of any date) on the date hereof is $87,541,008;

WHEREAS, the Holders of approximately $75,300,000 (or 86%) (i.e., not less than 66 2/3%) in aggregate principal amount of the Outstanding Notes) have validly delivered and not validly withdrawn Consents to the adoption of all of the Proposed Amendments effected by this Supplemental Indenture in accordance with the provisions of the Indenture, such amount of Consents having been certified in writing by Global Bondholder Services Corporation, the exchange agent for the Consent Solicitation; and such Consents have been delivered to the Trustee and Collateral Agent;

1

WHEREAS, having received the Collateral Release Requisite Consents, pursuant to Section 1002 of the Indenture, the Issuer desires to amend the Indenture, the Notes and the other Note Documents (the “Amendment”);

WHEREAS, in accordance with Section 1003 of the Indenture, the Issuer has delivered to the Trustee and Collateral Agent an Officers’ Certificate and an Opinion of Counsel with respect to this Supplemental Indenture on the date hereof; and

WHEREAS, pursuant to Sections 1002 and 1003 of the Indenture, the Trustee and Collateral Agent are authorized to execute and deliver this Supplemental Indenture.

NOW THEREFORE, in consideration of the foregoing and for other good and valuable consideration, the receipt of which is hereby acknowledged, in order to effect the Amendment, the parties mutually covenant and agree as follows:

ARTICLE I

Defined Terms

Section 1.1 Capitalized Terms. Capitalized terms used herein without being defined herein shall have the meanings assigned to them in the Indenture.

ARTICLE II

Amendments to Article 2—Definitions and Other Provisions of General Application

Section 2.1 Section 201 of the Indenture is hereby amended by deleting from such section the following defined terms: Action, Adjusted Consolidated Net Tangible Assets, After Acquired Property, Capitalized Lease Obligations, Communications Laws, Dollar Denominated Production Payments, Excluded Collateral, FCC, FCC License, Modified ACNTA, Modified ACNTA Prices, Net Working Capital, Permitted Liens, Production Payments and Reserve Sales, Related Person, Secured Obligations, Security Document Order, Volumetric Production Payments and any other defined terms references to which in the Indenture as amended by this Supplemental Indenture have been eliminated as a result of the Proposed Amendments effected by this Supplemental Indenture.

ARTICLE III

Amendments to Article 11—Covenants

Section 3.1 Section 1118 of the Indenture is hereby deleted and amended and restated to read in its entirety as set forth below:

“Section 1118. [Intentionally omitted].”.

ARTICLE IV

Amendments to Article 13—Security

Section 4.1 Section 1301 of the Indenture is hereby deleted and amended and restated to read in its entirety as set forth below:

2

“Section 1301. [Intentionally omitted].”.

Section 4.2 Section 1303 of the Indenture is hereby deleted and amended and restated to read in its entirety as set forth below:

“Section 1303. [Intentionally omitted].”.

Section 4.3 Section 1304 of the Indenture is hereby deleted and amended and restated to read in its entirety as set forth below:

“Section 1304. [Intentionally omitted].”.

Section 4.4 Section 1306 of the Indenture is hereby deleted and amended and restated to read in its entirety as set forth below:

“Section 1306. [Intentionally omitted].”.

Section 4.5 Section 1307 of the Indenture is hereby deleted and amended and restated to read in its entirety as set forth below:

“Section 1307. [Intentionally omitted].”.

Section 4.6 Section 1308 of the Indenture is hereby deleted and amended and restated to read in its entirety as set forth below:

“Section 1308. [Intentionally omitted].”.

Section 4.7 Section 1309 of the Indenture is hereby deleted and amended and restated to read in its entirety as set forth below:

“(a) [Intentionally omitted].

(b) Any release of Collateral permitted by Section 1305 shall be deemed not to impair the Liens under this Indenture and the Security Agreement and the other Security Documents in contravention thereof. Any certificate or opinion required under Trust Indenture Act § 314(d) may be made by an officer or legal counsel, as applicable, of the Company except in cases where Trust Indenture Act § 314(d) requires that such certificate or opinion be made by an independent Person, which Person shall be an independent engineer, appraiser or other expert selected by the Company.

(c) [Intentionally omitted].

(d) [Intentionally omitted].

(e) [Intentionally omitted].”.

3

Section 4.8 Section 1310 of the Indenture is hereby deleted and amended and restated to read in its entirety as set forth below:

“Section 1310. [Intentionally omitted].”.

Section 4.9 Section 1311 of the Indenture is hereby deleted and amended and restated to read in its entirety as set forth below:

“Section 1311. [Intentionally omitted].”.

ARTICLE V

Releases

Section 5.1 Without any further action by any party hereto, all Collateral securing the Obligations of the Issuer and the Subsidiary Guarantor under the Notes and the Indenture is hereby released, and the Trustee and the Collateral Agent are authorized and instructed to execute all releases, termination statements and other documents reasonably requested by the Issuer and the Subsidiary Guarantor to evidence such release and termination of all Security Documents.

ARTICLE VI

Effectiveness

Section 6.1 Effectiveness. This Supplemental Indenture shall be effective and binding immediately upon its execution and delivery by the Company, the Subsidiary Guarantor, the Trustee and the Collateral Agent, and thereupon this Supplemental Indenture shall form a part of the Indenture for all purposes, and every Note and Note Guarantee heretofore or hereafter authenticated and delivered under the Indenture shall be bound hereby. Except as modified and amended by this Supplemental Indenture, all provisions of the Indenture shall remain in full force and effect. Notwithstanding the foregoing, the provisions of Articles II through V hereof shall not become operative until immediately prior to the delivery of, as the case may be, the Total Consideration (as defined in the Statement) or the Exchange Consideration (as defined in the Statement) on the Settlement Date (as defined in the Statement).

ARTICLE VII

Miscellaneous

Section 7.1 Incorporation. All provisions of this Supplemental Indenture shall be deemed to be incorporated in, and made a part of, the Indenture, and the Indenture, as amended and supplemented by this Supplemental Indenture, shall be read, taken and construed as one and the same instrument.

Section 7.2 Third Parties. Nothing in this Supplemental Indenture, express or implied, shall give to any Person, other than the parties hereto and their successors under the Indenture and the Holders of the Notes, any benefit or any legal or equitable right, remedy or claim under the Indenture.

4

Section 7.3 Governing Law. THIS SUPPLEMENTAL INDENTURE WILL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF NEW YORK.

Section 7.4 Conflict with Trust Indenture Act. If any provision of this Supplemental Indenture limits, qualifies or conflicts with any provision of the Trust Indenture Act that may not be so limited, qualified or conflicted with, such provision of the Trust Indenture Act shall control. If any provision of this Supplemental Indenture modifies or excludes any provision of the Trust Indenture Act that may be so modified or excluded, such provision of the Trust Indenture Act shall be deemed to apply to the Indenture as so modified or to be excluded by this Supplemental Indenture, as the case may be.

Section 7.5 Counterparts. The parties may sign any number of copies of this Supplemental Indenture. Each signed copy shall be an original, but all of them together represent the same agreement. The exchange of copies of this Supplemental Indenture and of signature pages by facsimile or electronic (including in “.pdf” or “tif” format) transmissions shall constitute effective execution and delivery of this Supplemental Indenture as to the parties hereto and may be used in lieu of the original Supplemental Indenture for all purposes. Signatures of the parties hereto transmitted by facsimile or electronically (including in “.pdf” or “tif” format) shall be deemed to be their original signatures for all purposes.

Section 7.6 Effect of Headings. The Article and Section headings herein are for convenience only and shall not affect the construction hereof.

Section 7.7 The Trustee and Collateral Agent. The Trustee and Collateral Agent shall not be responsible in any manner whatsoever for or in respect of the validity or sufficiency of this Supplemental Indenture or for or in respect of the recitals contained herein, all of which recitals are made solely by the Issuer.

Section 7.8 Successors. All agreements of the Issuer in this Supplemental Indenture shall bind its successors, except as otherwise provided in this Supplemental Indenture. All agreements of the Trustee and Collateral Agent in this Supplemental Indenture shall bind their successors.

Section 7.9 Severability Clause. In case any provision in this Supplemental Indenture shall be invalid, illegal or unenforceable, the validity, legality and enforceability of the remaining provisions shall not in any way be affected or impaired thereby.

[Remainder of page intentionally left blank.]

5

IN WITNESS WHEREOF, the parties hereto have caused this Supplemental Indenture No. 2 to be duly executed as of the date first written above.

[Signature Page to Supplemental Indenture No. 2]