Kenmore - Only At Lowe's
Lowe's might be a good candidate for making Kenmore their own house-brand. They are currently the largest (or nearly) retailer for Whirlpool appliances and could source Kenmore exclusively, providing consistency and predictability for customers. They have the potential sales numbers to develop and commission brand-only features similar to what Sears did with KM.
A big problem for anyone who acquired the name is, as Martin pointed out, there is a lot of crap with the KM sticker already on it that would need to be supported through end of warranty period, parts-availability requirements etc. Another problem, probably the biggest, is service and support after the sale for a new, exclusive line. Sears had that infrastructure in place for decades, no matter the manufacturer. Lowe's or _______ would need to build that, a huge undertaking and likely a large initial outlay of capital. They could contract the supply and in- field work out to a third party, which may cause (more) customer confusion and headaches.
Perhaps the best thing in the long run would be to sell the Kenmore name off to a foreign company, for cheap. Then at least we'll still have a sense of sentimental angst everytime we see dorm refrigerators, disposable toasters and blenders and hotplates at WalMart.