Fractional Reserve Banking

Fractional Reserve Banking is the practice whereby a bank holds reserves that are a fraction of its on-demand liabilities. It contrasts with a Full Reserve Banking system in which banks must hold reserves for 100% of on-demand liabilities.

Holding only a fraction of on-demand liabilities means that in the event of a bank-run the bank is mathematically unable to meet its obligations.

Put simply: a fractional reserve bank (or exchange) faced with a bank run will not be able to give back 100% of their bitcoins to users and will go bankrupt.