I'm ignorant as to how BTC exchanges work. Is there a market maker providing liquidity or do the exchanges take inventory themselves? Any info for this would

I'm ignorant as to how BTC exchanges work. Is there a market maker providing liquidity or do the exchanges take inventory themselves? Any info for this would be appreciated. Insofar as uneducated guesses go, I suspect they are facing a "bank run" liquidity crisis based on them taking inventory and not having the capital to accommodate withdrawals.