It is narrated from Hazrat Ibn Abbas (may Allah be pleased with them both) that a man came to the service of the Prophet (peace and blessings be upon him) and said, "My sister has passed away and she had not performed Hajj. Should I perform Hajj on her behalf?" The Prophet (peace and blessings be upon him) said, "What do you think, if she had a debt, would you pay it off?" Surely, Allah is more deserving that His right be fulfilled.

It is narrated from Hazrat Ibn Zubair that a man came to the service of the Prophet (peace and blessings be upon him) and said, "My father has passed away and he had not performed Hajj. Should I perform Hajj on his behalf?" The Prophet (peace and blessings be upon him) asked, "Are you his eldest son?" The man replied, "Yes." The Prophet (peace and blessings be upon him) said, "Then perform Hajj on behalf of your father. What do you think, if your father had a debt, would you not pay it off?"

Hazrat Ata says that Hajj may be performed on behalf of the deceased even if he did not make a will for it.