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In a letter to Sears Holdings Corp. (NASDAQ: SHLD) dated last Friday, ESL Investments recommends that the company sell off its Kenmore appliance brand, its home improvement business (SHIP) and its Parts Direct business. ESL is the largest shareholder in Sears and one of its largest lenders. Eddie Lampert is also chief executive officer of both companies.

Not surprisingly, perhaps, ESL suggests that because Sears has been unable to find a buyer for these assets “on acceptable terms,” ESL believes Sears “should aggressively pursue a divestiture of all or a portion of Kenmore, SHIP, and Parts Direct.” It just so happens that ESL is interested in “participating in such divestitures.”

ESL offered to submit a bid for the Kenmore brand “[i]f Sears believes it would be helpful.” ESL also submitted a non-binding indication of interest to acquire SHIP and Parts Direct at an enterprise value of $500 million. Sears sold its Craftsman tool brand to Stanley Black & Decker for $900 million in early 2017; the Kenmore brand is worth at least that.

But the biggest part of the offer may be this:

Additionally, if requested by the Sears Board of Directors, ESL also would be open to making an offer for Sears’ real estate (including the assumption of the $1.2 billion of debt obligations secured by such real estate), with the expectation of entering into an ongoing master lease for some or all of the stores to allow for their continued operation.

With a market cap of about $340 million at Friday’s closing price, that may turn out to be an offer the Sears board can’t refuse.

If ESL gets what it wants — and it’s hard to believe there be a lot of competition for anything but the Kenmore brand — the only thing left of Sears will be its name and some Kmart stores that probably have a short shelf life.

Sears stock traded up as much as 12% in Monday’s premarket and traded up around 8% shortly after the opening bell at $3.25, in a 52-week range of $1.99 to $13.94. The 12-month price target on the shares is $2.00.