Why would the exchanges not have the required funds to pay out? If you sell your bitcoins on an exchange, there must be a buyer with fiat on the exchange ready to buy it.
An exchange can have $10M in ExchangeUSD IOUs, but actually only have $5M in USD to pay out. This fractional reserve system (or in this example, probably insolvency) works so long as there isn't any kind of "bank run" on the exchange.
MtGox and BTC-e (maybe BTC-e still does - Idunno) used to have "code money." That is, you could withdraw fiat and BTC in the form of GoxUSD or GoxBTC - debt notes, represented by a hash, similar to Bitcoin. You could trade these notes around, and they offered excellent advantages, but also the very serious drawback that Gox may not honor the IOUs. These IOUs, it should be noted, are effectively the same as the balance you see in your account on an exchange -- they're not necessarily representing actual money. When Gox started issuing these IOUs as a withdrawal method, there was a very slight premium over face value due to the convenience they offered. However, when Gox's future started looking uncertain, GoxUSD and GoxBTC started trading at a discount under face value. This was because the debt notes (the same as account balances in exchange accounts) may not have been fully backed by Gox's reserves. Gox eventually discontinued issuing these debt notes due to regulations.