Some people want to sell BTC short (this means betting on a price decline).  These short sellers will pay to borrow your BTC, in order to sell them with the hope of buying those coins back later at a lower price.  So someone could setup a bank that offers interest to depositors, paid by the people who borrow BTC to sell short.  Those "borrowing" the BTC might not need to physically hold the coins if they are to be immediately sold short into the market.  This would prevent people from running off with depositors' coins.  However there will need to be a lot of collateral on hand from the short seller, otherwise if the price of BTC goes up quickly, there could be problems for the bank and the person who loaned the BTC.