UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

SCHEDULE 13D/A

Under the Securities Exchange Act of 1934

(Amendment No. 20)*

THE HALLWOOD GROUP INCORPORATED

(Name of Issuer)

Common Stock, par value $0.10 per Share

(Title of Class of Securities)

406364 30 7

(CUSIP Number)

Anthony J. Gumbiner

3710 Rawlins, Suite 1500

Dallas, Texas 75219

Copy to:

W. Alan Kailer, Esq.

Hunton & Williams LLP

1445 Ross Avenue, Suite 3700

Dallas, Texas 75202-2799

(214) 468-3342

(Name, Address and Telephone Number of Person Authorized to Receive Notices and Communications)

February 7, 2014

(Date of Event Which Requires Filing of This Statement)

If the filing person has previously filed a statement on Schedule 13G to report the acquisition that is the subject of this Schedule 13D, and is filing this schedule because of §§240.13d-1(e), 240.13d-1(f) or 240.13d-1(g), check the following box.  ¨

Note: Schedules filed in paper format shall include a signed original and five copies of the schedule, including all exhibits. See §240.13d-7 for other parties to whom copies are to be sent.

The information required on the remainder of this cover page shall not be deemed to be “filed” for the purpose of Section 18 of the Securities Exchange Act of 1934 (“Act”) or otherwise subject to the liabilities of that section of the Act but shall be subject to all other provisions of the Act (however, see the Notes).

Schedule 13D

This Amendment No. 20 to Schedule 13D amends the Schedule 13D (the “Schedule 13D”), filed by Hallwood Trust (formerly the Alpha Trust), a trust formed under the laws of the Island of Jersey, Channel Islands (the “Trust”), and Anthony J. Gumbiner, and is being filed pursuant to Rule 13d-2 of the General Rules and Regulations under the Securities Exchange Act of 1934, as amended (the “Act”). Unless otherwise indicated, all capitalized terms used, but not defined herein, have the meanings ascribed to such terms in the Schedule 13D. “No material changes” means no material changes to the response contained in the Schedule 13D previously filed.

Item 1. Security and Issuer.

This Amendment No. 20 to Schedule 13D relates to the Common Stock, par value $0.10 per share (the “Shares”), of The Hallwood Group Incorporated, a Delaware corporation (the “Company”), and amends and supplements all information contained in the Schedule 13D.

Item 2. Identity and Background.

No material changes.

Item 3. Source and Amount of Funds or Other Consideration

No material changes.

Item 4. Purpose of the Transaction

Item 4(a)—(j) is amended to include the following:

The Reporting Persons previously filed Amendment No. 19 to the Schedule 13D.

On August 23, 2013, Plaintiff Gary L. Sample (“Plaintiff”) filed a purported class and derivative action in the Court of Chancery of the State of Delaware (the “Court”) against the parties to the Merger Agreement and certain directors and officers of the Company (collectively, the “Defendants”), asserting, among other things, that the Merger Consideration (as defined in the Merger Agreement, as amended by the Amendment) was unfair and did not reflect the true value of the Company and all of its assets (the “Litigation”).

On February 7, 2014, Plaintiff and the Defendants (together, the “Parties”) entered into a Stipulation of Settlement (the “Stipulation”), by and through their respective attorneys, whereby the Parties agreed that, in order to resolve the Litigation, the parties to the Merger Agreement would amend the Merger Agreement to increase the Merger Consideration by $3.00 per share, from $10.00 per Share to $13.00 per Share, less any incentive payment that may be awarded by the Court to the Plaintiff and less any attorneys fees that may be awarded by the Court to Plaintiff’s counsel in accordance with the Stipulation. The Defendants specifically deny that they have engaged in any wrongdoing, deny that they committed any violation of law, deny that they breached any fiduciary duties, and deny liability of any kind to Plaintiff, the Company, or its stockholders. The increased Merger Consideration will be paid if the settlement set forth in the Stipulation (the “Settlement”) is approved by the Court and the Merger (as defined in the Merger Agreement) is consummated pursuant to the terms of the Merger Agreement as amended by the Second Amendment to the Merger Agreement, which was entered into by the Company, Parent, and Merger Sub as of February 7, 2014 (the “Second Amendment”).

If the Settlement is approved by the Court, all known and unknown claims against the Defendants relating to the Litigation will be released, including derivative claims. If the Court does not approve the Settlement, the Settlement and any actions to be taken with respect to the Settlement will be of no further force or effect and will be null and void, provided, however, that any amendment to the Merger Agreement entered into by the parties thereto shall remain in effect. In the event that the Court does not approve the Settlement, the parties to the Merger Agreement have agreed to proceed with the consummation of the Merger based on the original merger consideration of $10.00 per Share, without the $3.00 per Share increase to the Merger Consideration contemplated by the Second Amendment, which would involve the resolicitation of stock holder approval at such price.

This summary above does not purport to be complete and is qualified in its entirety by the Stipulation attached hereto as Exhibit 1 and the Second Amendment attached hereto as Exhibit 2, each incorporated herein by reference.

Item 5. Interest in Securities of the Issuer

No material changes.

Item 6. Contracts, Arrangements, Understandings or Relationships With Respect to Securities of Issuer.

Item 6 is amended to include the following:

The description of the Stipulation and the Second Amendment in Item 4 above is incorporated herein by reference.

Item 7. Material to be Filed as Exhibits.

Item 7 is amended to include the following:

SIGNATURE

After reasonable inquiry and to the best of my knowledge and belief, I certify that the information set forth in this statement is true, complete and correct.

Date: February 12, 2014