“There are not strong reasons to be optimistic,’’ said Alan Treadgold, a retail expert at PA Consulting. “You exit the stores that are not viable. You manage the debt. But it still leaves the fundamental question: What is the purpose of Sears?”

In recent years, bankruptcy has not been kind to old-school retailers seeking a second life.

Toys “R” Us had hoped to cut its debts and reorganize as a smaller, more nimble company when it filed a Chapter 11 case last September. But rather than keeping the company going, its lenders decided they could recoup more by putting up its toys in a fire sale and shutting down all its stores. The clothing chain Bon-Ton also liquidated earlier this year and closed all its stores.

Sears could follow a similar path, particularly after Christmas when its stores have finished selling out their holiday inventory and will be less productive.

The one wild card is Mr. Lampert, who has continued to sink money into the company despite long odds.

In bankruptcy documents, Sears said Mr. Lampert’s hedge fund was willing to make the opening bid to essentially buy the company’s 400 most viable stores and keep them going.

In one filing, the company’s chief financial officer, Robert A. Riecker, said the hedge fund’s “support has ensured that the company’s doors remain open, and over 68,000 individuals remain employed.”

But Mr. Lampert may have other reasons to make sure Sears keeps the lights on. He is the chairman of and a large investor in Seritage Growth Properties, a real estate company that owns 230 former Sears properties. Sears pays rent to Seritage and a liquidation could imperil that revenue.