By Michigan State Law:
1. How long after an account closes are banks required to keep signature cards on file?
2. Are banks required to produce signature cards on demand?
3. IF a bank cannot produce a signature card what other means does a bank have to verify account signatures?

Questions 1 & 2 I can't help.

Question 3 If it is a checking account they will compare the signature to previous checks. Since the signature card is filed at the branch where the account was opened this is the easiest way to verify the signature.

#1 might well be a bank policy. #2 is no, they do not have to produce the card for a consumer.