In rare cases the FDIC cannot find a buyer for an insolvent bank and might have to liquidate its assets (i.e. sell the assets). When that scenario occurs, the depositors would not risk losing any of their money.
The deposit liabilities of the bank have the guarantee of the FDIC and ultimately the backing and guarantee of the US taxpayers. Although the government has no obligation to protect shareholders or the makers of notes owned by this bank, they have a very real and important obligation to protect the deposit liabilities of the bank. Those deposit liabilities make up a significant portion of the nations money supply.