The company’s largest creditors will ultimately decide whether they would recover more money by letting Mr. Lampert keep the company going or by selling Sears off piecemeal.

On Friday, Sears determined that Mr. Lampert’s bid was not adequate, which led analysts and investors to believe that the retailer was headed toward a fire sale.

But lawyers for a committee of independent directors and Mr. Lampert negotiated through the weekend and Monday in an effort to save the company. The bankruptcy hearing, scheduled for Tuesday morning in White Plains, was delayed by three hours, while the two sides talked.

[Read more about what led Sears to a bankruptcy filing.]

To buy an extra week, Mr. Lampert, through his hedge fund ESL Investments, said he would put down a $17.9 million nonrefundable deposit — which is how much it will cost to keep Sears open through Monday’s auction.

This was an important concession to creditors, many of whom believe their losses mount every day that the company keeps its doors open.