This is the right way to do things.
The bank's IT department will be liable for all of her extra expenses, and the Bank's HR department should be involved, as well as the bank's insurance company.
No proper off-boarding procedure, which means that they cannot confirm that everything was done properly.
If the banks IT department are screwing up like this, then where else are they failing to do their job.
Report them, and act as whistleblowers to the insurance company.