IE isn't going away, so I think its in everyone's best interests that they are actively involved in the browser competition.
Why so sure it's not going away?
Put yourself in their shoes and attempt to come up with one good reason why they wouldn't want to keep making a browser. They rarely get out of markets they're already in, and I don't think they're just going to forfeit a dominant market position just because the competition is better (see Windows).
IE as an application is definitely here to stay, but I wouldn't consider it too off the wall for them to switch to one of the OSS HTML / JS engines. I don't expect it, but it wouldn't surprise me.
I didn't say they'd stop making a browser, I'd suggest people will just stop using it.
If they do their classic strategy, it'll be "embrace and extend" with Javascript. The only problem is that their marketshare has eroded to the point where this might just cause their marketshare to erode even more.