It matters. Do you want digital bits? You can have all the bits you want, and so can the entire population of the city.
Do you want physical cash? Well, of the bank is printing its own, they can hand out whatever they can print.
If you expect fiat currency (e.g. USD) or precious metals, then withdrawals are all limited by what the bank has on-hand, or can get quickly. Assuming this is what you’re asking about, it would be a “run” on the bank, they’d close up shop for the day, and it would affect the faith the population has in the monetary supply.