If exchanges hold BTC for their customers, is it possible they are selling more than what they have?

This question came up to me right now.

Lets say Binance has 100 BTC in their possession and they're "selling" the BTC to their customers, or they're holding for them. Is it possible that they are allocating 1 BTC for two different people that have 1 BTC each?

Is that possible? Can they be somewhat creating imaginary BTC?

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Now if everyone would take all BTC of Binance, what would happen? Would they have all the BTC needed for that or they would be lacking some?

If this is true, we are saying that theoretically there is more than 21 Million BTC because exchanges are selling more than what they have, thus we have a lot more BTC than the supply available, which means we have imaginary BTC.