Bankrupt retailing icon Sears Holdings Corp. (SHLDQ)  has avoided liquidation for at least a few more days, with a court agreeing Tuesday to give company Chairman Edward Lampert's ESL Investments hedge fund until Wednesday to submit a revised offer to buy the chain as a going concern. However, Sears will still move forward with a Jan. 14 asset auction that will include Lampert's bid as one possible option. 

ESL had offered $4.4 billion for the chain, but the hedge fund and Sears management couldn't agree on terms. However, U.S. Bankruptcy Court Judge Robert Drain agreed with plans to give Lampert's fund until 4 p.m. ET Wednesday improve its bid. Lampert's offer will include a $120 million cash deposit, $17.9 million of which is non-refundable, Sears lawyer Ray C. Schrock said during a hearing before Drain in suburban New York.

The Jan. 14 auction could spell an end to Sears' 126-year history. After years of slow declines, Sears closed even more stores in recent months after filing for Chapter 11 bankruptcy protection in October. 

The company's assets and about 68,000 jobs are at stake if the company completely shuts its doors. However, news of the temporary reprieve sent Sears stock up as much as 30% Tuesday to 39 cents a share. Still, the stock pulled back to just 34 cents a share shortly after 2 p.m. ET.

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(This story has been updated.)