If the head looks wilty it might die. When I got mine, 4 heads were fine and the smallest was wilty. I was told to cut it off in the middle of the trunk to save it. After about 3 weeks, it grew new little hands and is doing great now.
Don't do anything until you have heard from other people too b/c mine weren't purple, just darker/ shriveled. But supposedly if the top is not cut off, it can kill the whole coral if indeed it is dying.