> Sets the living entity's leash.
Implies the leash is an entity in itself. (Possible revision: "Sets what entity this entity is leashed to")

> Setting the leash to null will remove the leash without dropping it.
Again, implies setting this "leash" entity to null will drop it.

You use the word "leash" as though it is an entity. 

However the simple fact that 2 people disagree what the JavaDoc implies is a good indicator it needs revising :P