Great question.
One that I can't answer. My favorite player has never left my favorite team. Then again, many times, my favorite player hasn't been on my favorite team.
However, I can think of one case that fits pretty closely, from when I was a Phoenix Suns fan back in the early '80's. Phoenix traded Paul Westphal, a player I really, really liked, for Dennis Johnson, a player I really, really *DIDN'T* like. I stayed a Suns fan, but not for long. I actually switched teams - to the team that *DID* have my favorite player (Bobby Jones, of Philadelphia). But I've always had a soft spot for the Suns, which was my first team, from the 1979 season.
Phoenix trading away Westphal and getting Johnson was a move that poisoned me to the team. And, of course, I didn't go to the Sonics, following Westphal, since I hated the Sonics (in no small part because of Johnson).
I think a person's favorite team losing a favorite player would probably make folks like me go to a different team altogether - one without the player. I suspect there will be a bit of bitterness at the abandonment, and a bit of resentment at the team not retaining them.
That said, I can see a lot of Cleveland fans abandoning the team in favor of some team that they don't find objectionable. In other words, not Miami, and probably not Boston, not Orlando, and, for the older fans, not Chicago. Could a lot of these fans become Oklahoma City fans, on the hope that Durant will overshadow James? I think so.