What you describe is a currency exchange risk, which would be the same of a bank holding a position in (for example) Japanese Yen but not covering it and holding their assets in USD instead.
The fraction reserve banking is a bit different issue, it's mostly about working in a single type of currency but backing short-term liabilities (e.g. account balances) with long-term assets (e.g. mortgage loans). So a customer A deposits 1 BTC and on-chain it gets transfered to the institution. Then when a customer B gets a loan of 1 BTC there's still just 1 on-chain BTC but 2 BTC-denominated IOUs, so the effective supply has doubled. Obviously, both of them can't withdraw the same coin at once, but the institution is not bankrupt as it has enough assets to cover all their debts, it may be temporarily insolvent though if a bank run happens.
The key difference from ordinary banking, of course, is that noone really takes loans denominated in BTC, so right now there's not much that an institution could have on the asset side other than "real" BTC. However, in a hypothetical world where BTC becomes the "mass market money" in some countries, then there would be BTC-denominated loans which would (among many other interesting effects) drive the pressure towards an equivalent of fractional reserve banking.
A clarification: IOUs are not money, bank deposits are. The money supply is the money issued by the central bank (aka monetary base) plus bank deposits.
The fraction reserve banking is a bit different issue, it's mostly about working in a single type of currency but backing short-term liabilities (e.g. account balances) with long-term assets (e.g. mortgage loans). So a customer A deposits 1 BTC and on-chain it gets transfered to the institution. Then when a customer B gets a loan of 1 BTC there's still just 1 on-chain BTC but 2 BTC-denominated IOUs, so the effective supply has doubled. Obviously, both of them can't withdraw the same coin at once, but the institution is not bankrupt as it has enough assets to cover all their debts, it may be temporarily insolvent though if a bank run happens.
The key difference from ordinary banking, of course, is that noone really takes loans denominated in BTC, so right now there's not much that an institution could have on the asset side other than "real" BTC. However, in a hypothetical world where BTC becomes the "mass market money" in some countries, then there would be BTC-denominated loans which would (among many other interesting effects) drive the pressure towards an equivalent of fractional reserve banking.