I hold onto Doubie unless someone makes a crazy offer. Casey Fossum "the Blade" was ok (he's great in MVP 04 for Xbox), but Doubie has a better build. I'm in it for the next few years with him. If I was the Cubs and had Doubie, I'd probably try and sell high.
I'd do it.
I only keep Doubront as he's cheap and productive. Not sure he'd have trade value that would bring a substantial return. He's worth more to the Sox.