If the owner gives the notice, then they can pay rent only till the date they stay.
If the tenant gives the notice, the tenant needs to pay rent for the whole notice period. This cam only be waived if they find a replacement tenant.
If the tenant does not give notice AND does not renew, then he still must pay rent for the notice period which will start on the date of expiry of the agreement. Please see clause 25 of the sample tenant agreement:
If the tenant asks you to adjust the Rent with the SD for the notice period, please tell them that this is not possible. Rent has to be paid as per the due date as mentioned in clause 7, and any violation is considered a breach of the agreement and the consequences for the same are mentioned here.