I've seen players who weren't willing to extend, change their mind when traded, though I think only when they were insisting on FA due to being arb'd too many times. I assume that the reverse could be true, that a player could change his mind and insist on FA, though I've not seen it happen.
In my experience, almost always when a player is traded they will maintain their current position on their pending FA. IE, if they're willing to resign, they still will be after being traded, and vice versa.
Somebody please correct me if I'm wrong.