If there are joint lessees on a safe deposit box and a deputy is named, can the deputy continue to access the box upon the death of one of the lessees? I am referring to the terms and conditions on the box and it indicates states "If any of you die, the surviving lessees and only the surviving lessees will continue to have rights under the lease and to the safe deposit box." Therefore it appears the deputy's power to act ceases.

I am just curious if this is normal? Technically at that point, the box could be closed by the surviving lessee and a new box opened designating that deputy again?

State law issue.

Also take a look at the document naming the deputy. Does it have language that addresses your question? But as with virtually every other safe deposit box question, state law controls.