Sears is a jack of all trades store that doesn't have much value these days. Before Home Depot and Lowes were everywhere, Sears was a good option for appliances, lawn care, power tools, etc. They were good for fitness equipment before Dicks. They were good for electronics before Best Buy. I suspect a place like Kohls took over their clothing audience as well.
Of course the internet didn't help them much either.
I'm sure someone will gladly buy up Craftsmen when it goes up for sale but I agree with you that it's their only exclusive asset that sets them apart.