A question to the traders

I've learned that everytime someone wants to open a short position they basically borrow the asset, buy it later at a lower price and give it back.

The question to the traders: What happens if the exchange doesn't have anymore btc? Will it still be possible to short btc? Normally it shouldn't be possible, however I have the feeling this is all just theory and in reality it's just a numbers game they will just continue to play.

What do you think? Or do you know how it works for sure?