Exhibit 10.1

SECOND AMENDMENT TO RESTRUCTURING SUPPORT AGREEMENT

This SECOND AMENDMENT (this “Second Amendment”) to the Restructuring Support
Agreement, dated as of October 20, 2016 and as amended by that certain First
Amendment to Restructuring Support Agreement, dated as of November 4, 2016 (the
“First Amendment”), by and among (i) the Stone Parties (as defined therein) and
(ii) the Consenting Noteholders (as defined therein) (together with the
schedules, annexes and exhibits (including the term sheet) attached thereto, as
amended by the First Amendment, the “Restructuring Support Agreement”), is being
entered into as of November 9, 2016, by and among (i) the Stone Parties (as
defined in the Restructuring Support Agreement) and (ii) the undersigned
Consenting Noteholders (as defined in the Restructuring Support Agreement). This
Second Amendment collectively refers to the Stone Parties and the Consenting
Noteholders as the “Parties” and each individually as a “Party.” Capitalized
terms used but not defined herein shall have the meanings ascribed to them in
the Restructuring Support Agreement.

WHEREAS, the Parties desire to further amend the terms of the Restructuring
Support Agreement to further extend the deadline for commencement of the
solicitation in respect of the Plan as set forth on Schedule 1 from November 10,
2016, to November 15, 2016 (collectively, the “Proposed Amendment”);

WHEREAS, pursuant to Section 28 of the Restructuring Support Agreement, the
Proposed Amendment requires the prior written consent of the Stone Parties and
the Required Consenting Noteholders; and

WHEREAS, the undersigned Consenting Noteholders, taken as a whole, satisfy the
definition of Required Consenting Noteholders as it applies to the Proposed
Amendment.

NOW, THEREFORE, in consideration of the promises, mutual covenants, and
agreements set forth herein, and for other good and valuable consideration, the
receipt and sufficiency of which are hereby acknowledged, each of the Parties,
intending to be legally bound, hereby agrees as follows:

 

  1. Amendment to Schedule 1. The first paragraph (paragraph (a)) of Schedule 1
of the Restructuring Support Agreement be, and it hereby is, amended and
restated in its entirety to read:

“the Stone Parties shall commence the solicitation in respect of the Plan, no
later than November 15, 2016;”

 

  2. Miscellaneous.

 

  a.

Sections 15 (Fees and Expenses), 16 (Consents and Acknowledgments), 18 (Survival
of Agreement), 19 (Settlement), 20 (Relationship Among Parties), 21 (Specific
Performance), 22 (Governing Law and Consent to Jurisdiction and Venue), 23
(WAIVER OF RIGHT TO TRIAL BY JURY), 24 (Successors and Assigns), 25 (No
Third-Party Beneficiaries), 26 (Notices), 28 (Amendments), 29 (Reservation of
Rights), 30 (Counterparts), 31 (Public Disclosure), 32 (Creditors’ Committee),
33 (Severability), 35 (Time Periods),

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  36 (Headings), 37 (Interpretation) and 38 (Remedies Cumulative; No Waiver) be,
and each of them hereby is, incorporated by reference, mutatis mutandis, as if
such provisions were set forth fully herein.

 

  b. This Second Amendment, together with the Restructuring Support Agreement,
as amended hereby, constitute the complete and exclusive statement of agreement
among the Stone Parties and the Consenting Noteholders with respect to the
subject matter hereof and thereof, and supersede all prior written and oral
statements by and among the Stone Parties and the Consenting Noteholders or any
of them.

 

  c. Except as specifically amended hereby, the Restructuring Support Agreement
shall remain in full force and effect.

[Signature pages follow]

 

2

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IN WITNESS WHEREOF, the Parties have executed this Second Amendment as of the
date set forth above.

 

STONE ENERGY CORPORATION, a Delaware corporation By:   /s/ Kenneth H. Beer  
Kenneth H. Beer, Executive Vice President and Chief Financial Officer STONE
ENERGY OFFSHORE, L.L.C., a Delaware limited liability company, by Stone Energy
Corporation, its sole member By:   /s/ Kenneth H. Beer   Kenneth H. Beer,
Executive Vice President and Chief Financial Officer STONE ENERGY HOLDING,
L.L.C., a Delaware limited liability company, by Stone Energy Corporation, it
sole member By:   /s/ Kenneth H. Beer   Kenneth H. Beer, Executive Vice
President and Chief Financial Officer

 

[Signature Page to Second Amendment to Restructuring Support Agreement – Stone
Parties]