In the Indian stock market system, shares are delivered to a demat account of the buyer in 2 trading days post transaction date. Brokers also permit the buyers to sell these shares before they have them in their demat account, provided that the exchange will deliver them in a timely fashion.
On the other hand, if the exchange is unable to deliver the shares to the buyer, it implies that the seller in this deal has failed to give the shares to the exchange. Failure to deliver shares is known as short delivery. When such a situation arises, the exchange organizes an auction for the same quantity of shares and delivers it to the respective buyer.
Short delivery can occur in stocks with low liquidity or if a short MIS/CO/BO has not been squared off in some situations.