CHICAGO — Earlier this month, Sears Holdings Corp. chairman Eddie Lampert was the victor in a bankruptcy auction for the U.S. department store operator with an improved takeover bid of roughly $5.2 billion, allowing the 126-year-old retailer to keep its doors open.

Lampert’s bid, upped from an earlier $5 billion offer, prevailed after weeks of back-and-forth deliberations that culminated in a days-long bankruptcy auction held behind closed doors. The billionaire’s proposal, made through his hedge fund ESL Investments Inc., will save up to 45,000 jobs and keep about 400 Sears and Kmart stores open across the United States.

The offer beat out a bid, which was supported by most Sears creditors and landlords, by Abacus Advisory Group to close all the stores and sell the inventory.

Subject to court approval, ESL will acquire substantially all of Sears’ remaining assets, including 425 stores, for about $5.2 billion. Sears’ other brands include its “Go Forward Stores,” Home Services business and Kenmore and DieHard brands.

The largest remaining question pertaining to the deal is Sears’ unsecured creditors, including Sears’ spinoff of Lands’ End and real estate investment firm Seritage Growth Properties, which are opposed to the bid.

The bankruptcy judge overseeing the case, Judge Robert Drain, will need to assess the merits of any objections at a hearing set for February 1 at the Southern District of New York Bankruptcy Court in White Plains, N.Y. Pending Drain’s approval, a deal will close on or about February 8.

Drain has so far shown an inclination to keep Sears alive. After disagreements between Sears and ESL in an auction for the retailer left the two in a stalemate earlier, Drain encouraged the parties to resume talks.

The Restructuring Committee of the board of directors said: “We are pleased to have reached a deal that would provide a path for Sears to emerge from the Chapter 11 process. Importantly, the consummation of the transaction would preserve employment for tens of thousands of associates, as well as the relationships with many vendors and suppliers who provide Sears with goods and services. We would like to thank our dedicated associates, vendors and partners for their continued support through this process and, most importantly, the members and customers we have the privilege to serve.”