MN is great at identifying half remembered faces, books and films so here goes...
First of all, it's NOT "It's a Wonderful Life" (1946) despite me thinking it is
It involves a "bank run" which is when people lose confidence in a small bank or savings and loan, and hoardes of people turn up demanding to withdraw all their cash, and the bank collapses because they don't have the cash reserves to pay everyone at once, even though its otherwise solvent. Bit like people causing last years fuel shortage by all filling their cars up at the same time!
In this film, people are queueing up to withdraw their money from a small family run bank, and a character gets to the front of the queue and asks to DEPOSIT some cash, very very slowly with lots of small change which takes so long that it is legitimately closing time before the Bank runs out of money.
I've Googled and can't find the film.