During 2017, shares of Sears Holdings (SHLDQ) have rallied repeatedly as the company has announced various moves to cut costs, raise cash, and extract value from its remaining assets. However, each rally has fizzled out, as Sears' underlying business trends remain dreadful.

This process played out again in miniature just in the past week. Sears stock jumped 20% at the opening bell on Thursday, after the company announced that it would sell Kenmore-branded smart appliances integrated with Amazon.com's (AMZN 1.60%) Alexa platform through the e-commerce giant's website. The stock has now given back all of those gains.

SHLD Price Chart

Sears Holdings Stock Performance. Data by YCharts.

Indeed, while a partnership with Amazon could boost sales for the Kenmore brand, it will further undermine the core Sears retail business. As a result, this deal isn't likely to help Sears Holdings avoid bankruptcy.

Teaming up with the enemy

Kenmore is a private brand owned by Sears. Historically, Kenmore products have had very limited distribution outside Sears stores. Nevertheless, Kenmore had a 27% share of the U.S. appliance market as recently as 2003.

More recently, with Sears in a downward spiral -- and closing lots of stores -- Kenmore's market share has plunged. That's a big reason why Sears is finally breaking with precedent and selling Kenmore-branded appliances through one of its most vicious competitors.

The exterior of a Sears store

Sears has been closing stores at a rapid pace. Image source: Sears Holdings.

Sears Holdings plans to eventually sell its full line of Kenmore home appliances on Amazon.com, while integrating all of its Kenmore smart appliances with Alexa. (For now, Sears has only listed a relatively small number of products for sale on Amazon.com.) Sears Home Services and Innovel -- two other Sears Holdings subsidiaries -- will provide delivery, installation, and extended warranty service for Kenmore products sold through Amazon.

Appliance sales haven't migrated online yet

By offering appliances for sale through Amazon.com, Sears Holdings will be able to expose a new set of consumers to the Kenmore brand. Furthermore, since Sears has negotiated to handle delivery and installation itself, the Amazon partnership could give a boost to Sears Holdings' relatively profitable services businesses.

That said, investors shouldn't expect Kenmore sales to suddenly surge now that Sears is selling appliances through Amazon.com. For one thing, the expanded distribution will to some extent cannibalize sales that otherwise would have been made directly through Sears.

Additionally, Amazon.com hasn't broken through in the appliance market yet. Last year, home improvement stores accounted for 45% of major appliance sales in the U.S. Sears, Best Buy, and Sears spinoff Sears Hometown and Outlet Stores account for a large chunk of the rest of the market. Given its track record in other industries, Amazon will surely continue to gain share in the appliance market, but it could be years before it is a major player there.

Good for Amazon and Kenmore -- not so good for Sears investors

In the past year or so, Sears Holdings CEO Eddie Lampert has made it a priority to increase the value of the Kenmore and DieHard brands and the Sears Home Services unit via partnerships or other strategic changes. The recent agreement with Amazon clearly fits into this framework.

Amazon will benefit from this deal, because Kenmore is still one of the top appliance brands in the U.S. Meanwhile, expanded distribution through Amazon.com should increase the value of the Kenmore brand.

However, this isn't likely to help Sears Holdings shareholders. The company continues to burn $1.5 billion-$2 billion of cash annually. Selling Kenmore appliances through Amazon isn't going to provide a sudden windfall that would halt this negative free cash flow. As a result, Sears Holdings still appears to be spiraling toward a bankruptcy filing that will wipe out ordinary shareholders.

By contrast, Sears Holdings' creditors -- including CEO Eddie Lampert -- could benefit if the Kenmore brand becomes more valuable. After all, it will be one more asset that Sears can sell off to recover some value for bondholders who would otherwise face steep losses in a bankruptcy scenario.