They are deemed closed out when there is a short delivery of shares and the exchange finds no new sellers in the auction markets. Instead of providing the shares to the buyer, the exchanges settle in cash based on the close out rate.
The stock that was short delivered will be closed out at the highest price in the exchange from the day of trade until the auction day, or 20 percent above the official closing price on the auction day, whichever is higher. This information is subsequently sent on to the buyer. Consider it as a form of compensation for the buyer in the event of non-delivery of shares.
As an example -

Assume you purchased 100 ITC shares at Rs. 700/- per share, and these shares were short delivered, causing you to miss T+2 delivery. The Exchange then conducts an auction in which it attempts to locate new sellers who can deliver 100 shares of ITC to you. The trade is completed by a close-out if there are no new sellers in the auction markets.
Assume that on the auction date (T+2) the official closing price of ITC was Rs. 800/-. In this situation, the Exchange would conclude the trade at Rs.960/- (20% higher than 800), and the defaulting stock seller would be responsible for an auction penalty of Rs.16,000/- (960-800*100). As a result, the bidder would receive a total of Rs 96,000/- (Rs 80,000, i.e. the closing price on the auction date + Rs 16,000, which is the auction penalty).
If the price of ITC had reached 980 (from the day of trade to the auction day), the close out is done at Rs. 980, not Rs. 960, because it is greater than the closing price + 20% auction penalty of ITC on the auction day. The buyer of the securities will be reimbursed with a credit of Rs.980 per share in such a circumstance.