Answer:
Consult with your state statutes regarding escheatment. Some states would not consider an automatic payment to be customer intitiated activity and consequently the account and contents of the box would be considered escheatable after the appropriate amount of time has passed.
In the event that this lack of customer activity does not trigger escheatment, you simply maintain the accounts until, a) an executor comes forward, b) the funds run out in the checking account and you end up escheating the contents of the safe deposit box.
First published on BankersOnline.com 4/15/13