Surely an exchange is just a trading platform provided to allow buyers to buy from sellers who want to sell...
They don't need any Bitcoins themselves, they just need to have enough sellers so that the buyers can always buy.

If someone wants to buy a very large amount that can't be satisfied by the sellers, then an unfulfilled order will be left over.  Or the price gets pushed up until it is fulfilled.  Due to arbitrage between exchanges, increases in price in one exchange will either be brought back down, or other exchanges will follow higher.

If I understood the question correctly!