A judge on Monday is expected to set a formal date to free Detroit from bankruptcy protection, which could come as soon as early December.

U.S. Bankruptcy Judge Steven Rhodes put the end of the nation’s largest municipal bankruptcy case in sight earlier this month when he approved the city’s debt-cutting plan.

The ruling came more than 15 months after the city filed for Chapter 9 amid population loss, spiraling debt and rising pension and health-care costs. The city earlier reached settlements with all of its major creditors.

The city’s restructuring roadmap calls for trimming from its balance sheet $7 billion, or more than one-third of Detroit’s estimated long-term debt. It was a rare milestone decision for cash-strapped cities, even among those that have sought bankruptcy protection.

Since its bankruptcy filing, the city has shown signs of improvement, but enormous challenges remain. The city remains one of the nation’s poorest and most unsafe. Neighborhoods outside Detroit’s central core are beset by joblessness, unused vacant land and underperforming schools.

Donald Trump, whose name remains on Atlantic City, N.J.’s Trump Taj Mahal, will ask a bankruptcy judge on Monday to allow him to pursue a lawsuit to reclaim the Trump brand from the remnants of the gambling operation.

Mr. Trump and his daughter, Ivanka, sued to get the Trump name off casinos they said were no longer fit to represent their luxury brand. Trump Entertainment Resorts Inc.’s bankruptcy filing stopped action in the suit and relegated Mr. Trump to the status of an unsecured creditor.

Mr. Trump has not been involved with the management of the company for years.

Hurt by growing competition in neighboring states, the New Jersey seaside strip of casinos has suffered a steep loss in gambling action. When Trump Entertainment closed the Trump Plaza, it was the fourth casino to shut down this year.

The fate of Trump Taj Mahal and the prospects of a reorganization hang on hopes of reeling in $175 million worth of tax and other aid from the state of New Jersey. Judge Kevin Gross has threatened to boot Trump Entertainment Resorts out of Chapter 11 protection due to the lack of a “reasonable likelihood of rehabilitation” for the gambling company.

Also Monday, Oklahoma peanut processor Texoma Peanut Co. will ask for final approval of a $40.5 million loan from Wells Fargo Bank to allow it to continue operating in bankruptcy.

Texoma filed for Chapter 11 protection earlier this month with plans to quickly sell its business. The Madill, Okla., company, which processes raw and blanched peanuts for distribution to snack and confectionary manufacturers around the world, hopes to hold an auction to sell its business by Dec. 15 and is actively looking for prospective buyers, according to court filings.

In court papers, Texoma President Alan Ortloff blamed the company’s financial trouble on a crop recession and mismanaged growth spurt that caused the company in fiscal year 2013 to swing to a loss of $4.42 million, from a profit of $12.2 million in fiscal year 2012.

Texoma’s business relies on the collection of peanuts directly from farmers in Oklahoma, which is the ninth highest-producing peanut state, Texas, the fourth-largest, and Mississippi, the seventh largest.

-Matthew Dolan, Peg Brickley and Sara Randazzo contributed to this article.

Write to Tom Corrigan at tom.corrigan@wsj.com. Follow him on Twitter at @TheTomCorrigan