Stock market is like any other markets where traders can exchange their stocks for money, vice versa. Whomever willing to buy the stocks blaces the orde to buy, the brokers will take it to the stock exchange. In the same way, the sellers will place the orders to sell, which will come to exchange via broker. The stock exchage will place all the orders in one common queue, where the sell orders are arranged in ascending order, and the buy orders in decending. Whichever orders are getting matched will be executed and settle will happen.
If there any problem in the settlement, then stock exchange has to take whole responsibility, at the end they have to complet the trade. If any traders having problem can be taken to SEBI which regulates entire stock markets in India.