Depends on the position. Obviously, trust is lost, so if they say something like "yeah, I stabbed you, but I'm still willing to work together", I'm not going to agree to moves that let them take more of my territory, even if that may cede the advantage to someone else.
If the stabbing places me in a position where I have a minimal chance of survival, my goal is simple: absolutely SCREW the person who stabbed me if at all possible. If that means throwing my centers to another player while I kamikazi on the stabber, so be it. If they whine and bitch that I could have helped them set up a stalemate position, but my perception was that my head was going on a pike anyway once that happened, then there is minimal motivation for me to aid them.
Hell, depending on my level of annoyance I may choose to throw the game to someone else even *if* there is a reasonable chance for survival. One of the things about this game is that the people you play with are *unpredictable*, so if someone assumes that I'm just going to take a stab and be a nice little puppet, watching them froth as things completely unwind for them is the best satisfaction I can get out of the game.