Dive Brief:

ESL Investments, the hedge fund run by Sears Holdings CEO Eddie Lampert, sent a letter to the department store retailer Monday suggesting that it divest Kenmore appliance brand as well as its home improvement business (Sears Home Services) and that unit's PartsDirect division

The letter, signed by Lampert, further noted that ESL would be an interested buyer in the assets. Lampert in the letter said ESL, which owns a majority stake in Sears, would pay $500 million cash for Home Services and PartsDirect. He also expressed willingness to bid on Kenmore, but did not outline terms or a dollar figure. ESL is also willing to buy up real estate properties — which are currently being used to secure some $1.2 billion in Sears debt — and then lease back the property to Sears .

. Lampert and Kunal Kamlani, president of the hedge fund and a Sears board member, would not participate in the discussions, according to a Sears press release. ESL has retained financial and legal advisors for a potential sale, and Lampert said in the letter that his fund is "prepared to move as quickly as possible to complete customary due diligence for a transaction."

Dive Insight:

In the sale of some of Sears' most valuable remaining assets, the retailer faces a fairly clear trade off. It can make the sales, bring money into the business (and to shareholders) and reduce its debt burden — potentially staving off bankruptcy, at least in the short term — but would lose some of the best parts of its rapidly shrinking business.

It's a tradeoff Lampert and the retailer have proven quite willing to make. The company has already shed hundreds of millions of dollars in owned real estate (also to a venture controlled by Lampert) and the beloved Craftsman brand. It's also shuttered hundreds of other stores and laid off many hundreds of employees, too, in an effort to reduce costs and profit losses by essentially liquidating the company.

Lampert said in the letter that his fund "believes that the exchange offer and the tender offer would be beneficial to the debt holders by providing liquidity, to Sears, and by reducing its debt obligations and to equity holders, by reducing risk and giving Sears time to pursue value maximizing strategies."

The sales of Sears' Kenmore brand — which has lost market share over the years though recently attempted to reboot through a partnership with Amazon —and home services business could be a major boost to the company's financial profile. Already this year, the retailer freed up some cash and reduced its maturities due this year through a distressed debt exchange.

The sales would also be yet another major twist in the slow-rolling saga of Sears' decline. A financial boost is needed to avoid bankruptcy, but the retailer also needs to stop the bleeding of its customer base. Sears' comparable sales fell a woeful 15.6% in the fourth quarter — and 18% at the flagship brand — which had blessed other department store chains with sales bumps.

With those sales Sears would move closer than ever to running out assets to sell, property to divest, stores to close, employees to layoff and debt it can restructure or refinance. And with each of those moves, it also risks running out of reasons for people to shop with the retailer at all.