You can't convert crypto into fiat. You can trade one for the other with someone but you cant convert them, it's not alchemy, it's just a change of ownership. Exchanges like BTC-e have bank accounts which people transfer by wire and other means funds into to purchase BTC-e "casino tokens" called USD/RUR/EUR which they can gamble and trade with other BTC-e users for fiat or crypto tokens. The bank account balance doesn't change for those trades, it only changes when people cash out their tokens or make a new deposit, or when BTC-e take their fees out, so the balance should be high unless seized. Same goes for their crypto wallets.
Unless an exchange is trading their bank account fiat and crypto coins on some other exchange.
Also it is impossible to know have people deposited more fiat then it was withdrawn or vice versa. Exchange running out of one currency is possible.