My understanding is that's the one thing that is not up for sale these days, and that all relevant discussions are regarding the spinoff of their core web businesses.
I don't know if tumblr is profitable, but it has many users.
edit: whoops this was already mentioned a number of times in other comments.
https://en.wikipedia.org/wiki/Yahoo!_Groups#Site_statistics
http://www.huffingtonpost.com/daniel-burrus/yahoo-groups_b_1...
I fail to believe that Yahoo, minus Ali Baba and Fantasy sports and similar bits, is actively NEGATIVE value. It might be poorly run and have the poor actions you're talking about. (okay, it DOES have the negatives you mention).
That doesn't mean what's there "should just die" - it's a business opportunity to take that and use it profitably.
But that's not what you're suggesting - doubling down by doing more of what they've been doing. This assumes that what they're doing has some useful foundation you can find and build on.
There are essentially zero Yahoo users, especially of any service that's remotely monetizable. People who use Yahoo are people whose ISP set it as their default homepage ten years ago.
You can hear the fail in their words. They're talking about retaining users, not offering value. They still want to be a portal (ie the base of every action you take), something users didn't want when it was new.
That's the business legacy you'd have to reverse before you stop producing negative-value, let alone actually produce something that may actually be valuable.