Real banks have other assets to cover their liabilities. Sure some of these assets are not liquid. Banks cannot ask people to pay off their mortgage instantaneously so if too many people try to redeem deposits all at the same time, the bank might have to ask some people to wait. But the banks always have enough assets so that in the longer term they can pay everyone.
Plus in times of crises the central bank might step in and allow commercial banks to swap their illiquid assets for cash thus providing the needed liquidity.
Plus in times of crises the central bank might step in and allow commercial banks to swap their illiquid assets for cash thus providing the needed liquidity.