The market-maker provides market liquidity and gives bid/ask price of one unique equity. Then what will happen to an equity in an exchange which has only one market-maker when that market-maker goes bankrupt? Who will take the role of the market-maker?
Market itself. Every market participant makes ask or bid offer with all of its trades (even with MKT order - it is dissolvable to LMTs for best price levels).
If you have enough participants you don't necessary need market maker because your spread will be tight enough. (not speaking about extreme high volatile situations - but market makers are actually using their agreed time to be out of market during that moments also)