If banks have 100% of the money secured, nobody should have trouble getting their money back even if every one of goes to the bank at the same time.
Now, if 99% of the money is secured and we all went to bank at the same time, 1% will not get their money. The banks rely on the idea that there will not be a bank run by everybody and they’ve figured the ideal ratio that they can have between keeping money in the bank and how much of that money they can loan out.
It works pretty much most of the time. Except when the bank gets greedy and goes out of ratio of what they can keep on hand and what they can loan out. I’m not saying that this would be the only reason why a bank cannot pay out a customer’s money from their account, but it is a big one. Bank executives put too much weight on profit and not enough on being an on-going concern.
A bank with $10 billion in reserves is not going to be able to pay out $10 billion in cash withdrawals even if all its reserves are invested safely. That's because the $10 billion in U.S. Treasury bills they have accumulated over time would only be worth $8 billion if they had to sell them off today -- due to the steep decline in their value as interest rates have risen. (Think of how much a long-term T-bill paying out 1.5% has lost in value when they are currently paying out 4%.)
THIS is why the U.S. government bails these banks out. The government isn't concerned about a run on the bank by its depositors to take all their cash out. It's concerned about banks being forced to sell off their U.S. Treasury bills at a steep discount just to meet even 80% of their deposit exposure.