When many customers of a bank are concerned about the safety of their money in that bank and withdraw their deposits this is called a Bank Run. As discussed in How Does Money Work – Fractional Reserve Banking most banks operate on a fractional reserve system. This means that they can loan out much more money than they actually possess. When all or many customers of a bank try to withdraw their money at the same time this lack of reserve money can become a major problem and default often occurs (default occurs when a debt repayment cannot be made by a debtor). One famous example of a Bank Run was the great depression in December 1930 money supply shrank because of bank runs 32% reduction from 1929-1933
After this, in the USA the Federal Deposit Insurance Corporation (FDIC) was created was created in 1933 to ensure people’s money in the bank. This is to used to stop banks going bankrupt by paying customers of a bank a certain amount per bank account (this is called a bailout).