NEW YORK — Sears received another lifeline Tuesday when the company’s chairman and largest shareholder promised to line up the necessary financing to keep the struggling chain afloat.

The reprieve came after what Sears lawyers described to a bankruptcy judge in New York as “round-the-clock” negotiations following the company board’s initial rejection of Eddie Lampert’s proposal, which sought to preserve 425 stores and 50,000 workers. According to lawyers close to the matter, one of the main sticking points was that the $4.4 billion bid, which included $1.3 billion in financing from three financial institutions, didn’t include cash.

The bid now requires Lampert to deposit $120 million by 4 p.m. Wednesday through his ESL hedge fund. The revised bid is not official, and will be evaluated in an auction set for Monday that will compete with other bids from liquidators.

The 11th hour negotiation is yet another twist in the rocky journey of Sears whose fate has been hanging in the wind, particularly since it filed for Chapter 11 bankruptcy on Oct. 15. As of the filing, the company had just under 700 stores and 68,000 workers.

Sears, which at one time was the largest retailer in the world, has been in a slow death spiral.

Under Lampert, Sears has bought time over the years by spinning off stores and putting on the block the brands that had grown synonymous with the company, such as Craftsman.