Exhibit 10.1

FOURTH AMENDMENT TO RESTRUCTURING SUPPORT AGREEMENT

This FOURTH AMENDMENT (this “Fourth Amendment”) to the Restructuring Support
Agreement, dated as of October 20, 2016, by and among (i) the Stone Parties (as
defined therein) and (ii) the Consenting Noteholders (as defined therein), as
amended by that certain First Amendment to the Restructuring Support Agreement,
dated as of November 4, 2016 (the “First Amendment”), that certain Second
Amendment to the Restructuring Support Agreement, dated as of November 9, 2016
(the “Second Amendment”), and that certain Third Amendment to the Restructuring
Support Agreement, dated as of November 15, 2016 (the “Third Amendment”)
(together with the schedules, annexes and exhibits (including the term sheet)
attached thereto, as amended by the First Amendment and further amended by the
Second Amendment and the Third Amendment, the “Restructuring Support
Agreement”), is being entered into as of December 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 Fourth 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 extend the deadline for commencement of the Chapter 11
Cases as set forth on Schedule 1 from December 9, 2016, to December 13, 2016
(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 second paragraph (paragraph (b)) 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 Chapter 11 Cases by filing bankruptcy
petitions with the Bankruptcy Court no later than December 13, 2016 (such filing
date, the “Petition Date”);”

 

  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

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  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), 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 Fourth 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 Fourth 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 Amendment to Restructuring Support Agreement – Stone Parties]