Just when you thought Sears Holdings Corp. was on its way out, the bankrupt department store retailer could be saved once again by a $120 million infusion from its Chairman Eddie Lampert.

Sears shares jumped 33% in afternoon trading Tuesday, after the potential Lampert rescue was revealed, reversing a loss of as much as 50% earlier in the session. The company’s stock has still plummeted 88.6% the past 12 months while the S&P 500 index SPX, +0.97%  has dropped 6.3% for the period.

But should Sears SHLDQ, +30.09%  liquidate, the question is whether the company still has anything of value to sell after years of unwinding.

“Our data from the holiday period show that overall customer usage of both Sears and Kmart has fallen, and perceptions of both brands are sharply down on last year’s low scores,” wrote Neil Saunders, managing director at GlobalData Retail, in a note published Tuesday. “In essence, there is simply very little equity left in the brand.”

“That said, there may be interest in elements of Sears’ business such as the automotive side, the online operations, the brands, and the various home services,” Saunders said. “As such, parts of Sears could live on even if the company as we know it will disappear.”

In large part, what once made Sears a powerhouse retailer disappeared long ago along with the company’s market value, which was $43.5 million on Tuesday afternoon. In its heyday, Sears’ market value hovered just below $30 billion, according to FactSet data.

Lampert’s bid would keep 425 Sears stores open. Those stores would still be an asset.

“The liquidation process opens up bidding to more possibilities,” said Philip Emma, senior analyst at DebtWire. “Value can be extracted in multiple asset sales.”

Sears is best known as a seller of things like tools and appliances, where some value might still be gleaned as well.

“The parts of the business that worked, such as it is was, are the hard-line businesses,” said Emma. “If Sears had any reason to continue to exist, it has been the appliance, tool, battery businesses.”

Sears has agreed to license the DieHard and Kenmore brands, has joined with Amazon.com Inc. AMZN, +1.66%  on tires and DieHard products and sold the Craftsman brand to Stanley Black & Decker Inc. SWK, +1.84%  in 2018.

What may be most valuable to the competition are the members of the Sears loyalty program, Shop Your Way.

“The number one challenge in the C-suite that I hear about is, ‘It’s so hard to generate loyalty today,’” said Corey Pierson, chief executive of Custora, a provider of cloud-based customer intelligence software. A competing retailer might be interested in snapping up those loyal customers with an offering and logistical support that’s similar or better than what Sears has been able to provide.

“You will have a pocket of customers that trust Sears,” Pierson said. The competition could be thinking, “How might another company take those relationships and build that business around it.”

Chuck Tatelbaum, director at the law firm of Tripp Scott, agrees that the loyalty program is strong. But at this point, most everything that Sears had has already been picked over.

“There is not an ounce of flesh left on the carcass,” he said. “If you compare a year ago to Toys ‘R’ Us, when they went out, people had good feelings about it.”

“Sears has been on its last legs for so long, there’s nothing of value anymore,” he said.