What happens to my box if my bank fails?
When an insured bank or thrift closes, the FDIC usually arranges for another institution to take it over, including branches where you might have a safe deposit box. In those situations, you should be able to conduct business as usual. If the FDIC cannot find a buyer for your bank, it arranges for you to remove the contents of your box so you can obtain a box at another institution, if you wish. This is done within a few days after the bank fails.
http://www.fdic.gov/CONSUMERS/consum.../sfdpstbx.html