I doubt they would have to resort to deposit insurance. Those loans have value -- they would either borrow from another bank (one of the central banks, or the Fed) against the value of those loans, or sell the loans.
Now this is another interesting thing -- the market value of the bank selling a loan fluctuates inversely with interest. If they have a loan that a customer is paying 8% on, then that loan has a market value much higher if current rates are 3%, and much lower if current rates are 12% (assuming the risk of the loan doesn't change -- that also affects its market value).
No need to be a literalist. My point being: the cash needed to cover withdrawals would have to come from outside the bank's own reserves in the scenario I described.
Now this is another interesting thing -- the market value of the bank selling a loan fluctuates inversely with interest. If they have a loan that a customer is paying 8% on, then that loan has a market value much higher if current rates are 3%, and much lower if current rates are 12% (assuming the risk of the loan doesn't change -- that also affects its market value).