Banishment, mostly.  I assume if The Agency is confident enough to take on vampires, werewolves and witches, they do so because they know a weakness that could serve as a leash.  In Moe's case, some serious restraints and an exorcism are a fool proof way to make him go bye bye, along with other violent measures.  

With the taking in of what one could only deem as anti-heroes among the horror fantasy types, I have to assume The Agency works almost like an old fashioned Suicide Squad.  A rule-bending tough as nail organization that can tame the traditionally evil or, at the least, misunderstood.

Moe is not a team player.  Moe is a player on a team.  The only thing you can trust in him is his reluctance to shorten his time on Earth.