Have you heard of a starfish eating fish?
I just checked on a few, they are Carnivores but it looks like they generally eat bi-valves, like clams. I imagine they would eat a dead or possibly dying fish.
Some one might be along to give their presonal experience or what they have learned.
Again, it is hard to determine what kind it is with out a picture.
Also, what are your water paramiters?
1. Post your test results
2. How many fish have died and in what period of time, what else do you have in your tank?
Let's back up:
1 How long has your tank been up and running?
2 How did you acclimate your wrasse?
You can update your "my info" to let others know what kind of equipment/critters and such you have in your tank, so you won't have to keep answering the same questions.
+++EDIT+++
I just now found that Green Serpent Starfish:
As juvenilles they are normally fine with all other inhabitants but as they grow in size they have been known to eat small fish that venture into their hiding spots.