Keep in mind that exchanges don't buy or sell bitcoins. They simply create a market where others can trade. However, they hold bitcoins, and that is where the typical problems can arise.

However, it is possible for an exchange to also secretly trade with bitcoins or fiat that it does not have because the exchange controls the accounting. Whether or not that becomes a problem for the exchange depends what happens to the price. If the price rises after you sell bitcoins you don't own or it falls after you buy bitcoins with fiat you don't own, then you can lose a lot of money. If the price moves enough, it will cause the exchange to fail when there is no longer enough fiat or bitcoins to support normal operations.