In the traditional system a bank could “fail” if it lent money and all of its original depositors withdrew all of their money. In theory because the bank has lent some of the money to others, it does not have enough on hand to “cover” all the deposits. Banks were required to maintain a certain percentage of their deposits as “reserves” so that they could cover withdrawals up to a certain point. The National Bank Act of 1863 had set the reserve requirement at 25%, but when the Federal Reserve bank was created the requirements were lowered to 13%, 10% or 7% depending on the type of bank. Obviously this was not enough to save banks during the Depression when they were subject to “runs.” As of March 2020 the reserve requirement has been reduced to zero, but deposits up to $250,000 are insured by the Federal Deposit Insurance Corporation.
The idea that a bank can go bankrupt if it cannot cover a run of withdrawals makes sense if all the depositors want currency and the currency in the vaults has been used to make the loans. However, if the loans and the bulk of the deposits are just bookkeeping entries, it might seem that the bank could just issue cashier’s checks to be deposited elsewhere and honored by the bank with additional bookkeeping entries even if it meant that the books at the bank temporarily showed a “negative balance.” How a bank “honors” a check it has issued when it has been deposited at another bank and submitted by that bank is part of the function of a central bank or the Federal Reserve bank in the US. Presumably having a “negative balance” even temporarily amounts to being “bankrupt.”

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