Along with its bankruptcy filing, the company said Monday that Eddie Lampert's hedge fund, ESL Investments, is now in talks to buy "a large portion of the company's store base," while other assets are expected to be put up for sale in the next few months. Lampert had served as CEO of Sears for the past five years until Monday, when he resigned from the role effective immediately as part of the retailer's restructuring plan. He will remain chairman.

Lampert has a controlling ownership stake in Sears, with a 31 percent stake, according to FactSet. ESL Investments owns about 19 percent.

"Over the longer term, it is still unclear what Sears hopes to accomplish," GlobalData Retail Managing Director Neil Saunders said.

"In our view, there is no clear path to success," he said. "The group has tried to shrink its way to profitability for years to no avail, so it is hard to see why pursuing the same strategy under the auspice of Chapter 11 would result in a different outcome. Further asset sales may reduce debt, but they would not put the company on a sound financial footing nor would they solve the operating losses the group is racking up."

—Reporting by CNBC's Lauren Hirsch and Lauren Thomas. Data visualization by CNBC's John Schoen. Data on Sears locations was provided by AggData.com, a business location data service that specializes in retail locations.

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