Answer:
Failure to change the locks raises your risk of wrongful access. If a former lessee had a copy of his key made before surrendering the box, he could theoretically have an easier time accessing that old box after you've leased it to Mrs. Jones, who stores her valuable jewelry in it.
You might be better off replacing the decrepit locks. That will reduce the chance that an old lock will fail in service, too.
First published on BankersOnline.com 5/26/08