Banking institutions in the United States are required to hold reserves—amounts of currency and deposits in other banks—equal to only a fraction of the amount of the bank's deposit liabilities owed to customers. This practice is called fractional-reserve banking. As a result, banks usually invest the majority of the funds received from depositors. On rare occasions, too many of the bank's customers will withdraw their savings and the bank will need help from another institution to continue operating; this is called a bank run. Bank runs can lead to a multitude of social and economic problems. The Federal Reserve System was designed as an attempt to prevent or minimize the occurrence of bank runs, and possibly act as a lender of last resort when a bank run does occur. Many economists, following Nobel laureate Milton Friedman, believe that the Federal Reserve inappropriately refused to lend money to small banks during the bank runs of 1929; Friedman argued that this contributed to the Great Depression.
The Wikipedia article says that there can still be a bank run even with the Federal Reserve, and then even imply that it may not lend money to all banks if all banks were to suffer a bank run, and the Federal Reserve will not repay some depositors if they were to lose money in a massive bank run crisis where everyone would retire their money. Is this true? I thought the system was set up to prevent bank run of any kind no matter the scale.