In the US, they would reopen your account without telling you and start charging you fees and/or interest on the amount they overpaid. I know this because it happened to me last year when American Express mistakenly refunded a credit to me twice when closing an account (one check and one bank transfer). I never even cashed the check but apparently that didn’t make a difference to them.
The cashier gave me all the cash I’d already taken from the account.