destroy() method V.S. finalize() method

I am creating a modification of the Singleton architecture.  I am only
permitting one of a specific object with specific attributes.  When I am
performing this function, I need to remove the object reference from a
hashmap when the object is destroyed by the user.  My question is this....
Should I place the code for removing the object reference from the hashmap
in the destroy() method, or the finalize() method?

My class is going to contain a static hashmap of objects with a key
reference object.  I am concerned that either the destroy() or finalize()
does not get called when a class is given a null reference.  I am thinking
that one of the methods will get used for the last instance of the class and
the other will be used for when each instance.

any insights?

Thanks

Mike