We have keys. In the event those are lost or destroyed, they will provide access to an approved list of individuals and drill the lock for $40.
Also they're small town banks, so that makes it easier as well. We don't really need to worry about providing ID, but if we did and couldn't access ID or something like that, we have four other people listed with access, one of which lives hours away in case of a disaster impacting everyone else on the list. They don't have keys but could get into it for us. So for a few hundred dollars, we're set and insured for the declared value of the contents of the boxes (250k max for another $15/year) if the banks are both destroyed as well!
Bank vault can be key+combination (eg three letters) or dual key or others. For example in a dual key: one key from the bank and one key being your own key.
If a key is lost, you go and prove your identity (easier if any bank employee is familiar with you) and ask for a new key. A date is set and a locksmith shall come, you are next to him and next to the bank employee while he uses the bank's key and lockpicks your lock. Then he configures it for a new key (or replace the lock).
It's cost you something like $300 or whatever.
Source: been next to locksmith opening a bank vault, twice, in two different countries. Once for a bank belonging to a deceased family member (we had the key but not the three-letters combination) and once not because I lost my key but because the bank's lock (on my vault) went defective.
So it's not "my key from the my vault at the bank melted during a housefire, so I can never access my vault at the bank anymore" nor is it "I forgot my three-letters combination, so until the end of the universe that bank vault shall stay locked".
In general, identity (the bank checking who you are) is often involved in regular unlocking and there will be an identity-only recovery procedure that will work even if you lose your usual credential (key, passcode, card, whatever). This may involve drilling a lock and the bill for that.
