What happens if your called back for a play for a character you don't?

What happens if your called back for a play for a character you don't?
I'm assuming you mean a character you don't want? If that's the case, then as an actor myself I can tell you that you should take the role regardless. First of all, portraying any character on stage gives you the opportunity to refine your acting skills. Secondly, if you don't take the role, you may not be called as quickly by the same production company for a role you do want in the future. Furthermore, if you truly love to act, then you take whatever is offered. Otherwise you really shouldn't be in the game.