Depends on who you ask really. A lot of people will frag off the good stuff to save it. I personally leave it alone for the most part because it will eventually grow back over the dead branches. Even if by this time next year it decides not to grow over the branches you could easily clip them off which is better than having a whole bunch of frags.
By leaving it, you do run the risk of losing the whole colony. I haven't had this happen to me on a large coral but smaller ones yes. The good thing about birdnest is that it's cheap....