In a normal bank run, the problem is that the people want the money back now but the bank has lend most of it and the money is locked in a 20 years mortgage. In some sense all the deposits of the bank are 100% backed. They just can't go immediately and reposes a house and send a bunch of brick to the people that want their deposits.

There are also some cases when the bank has no enough money (bad lenders selection, promised a too high interest rate, fraud, ...). In this case the deposits are not fully backed. But this is not the normal state of a bank.