Hi Susan,
Don't know about the cause, maybe another fish nipped it and then a bacterial infection set in?? At any rate, I'd be very careful with this fish because if you see a reddish patch at the base of the body where it meets the tail, that means you have a bacterial infection in the flesh. It can then go downhill very fast.
If it was caused just from nipping, and the water quality is good then it should regrow the tail eventually.
Only problem is if you have a high bacterial load in the water that gives opportunistic bacteria such as vibrio a foothold. But wrasse are very hardy. If it was my fish, and I was confident in the water quality I would leave it as is.
Sorry for the ambiguous reply,
Angie.