Dear unclaimed:

What ever you do, do not claim the items as museum property.  Try to notify
the party again via certified letter and state that unless notified otherwise
within 30 to 60 days you will be shipping their loan back to them.  Check
with your organization's legal advisor before proceeding.  We once had loans
dating back to 1939, and discovered that the grandchildren of the loanee had
claim on the items even though they had not checked on the loan for over 40
years.

Been there.