The scenario wherein shares are bought but not received by you within the set time limit T+2 working days(trade day + 2 working days) is known as short allotment. However, you would most probably receive the shares in your demat account within T+4 working days(trade day+4 working days).
In case of market shortage, the shares are allotted to the client in T+4 working days. If the purchase from the market is not possible, the client will receive a credit amount in his trading account for that particular share.