Firstly: One who dies not having performed their wajib Hajj
Hajj remains a duty upon one who dies not having performed his wajib Hajj. It is funded through his capital whether he indicated as much in his will or not. [1070] It is not a duty to perform Hajj on behalf of one who dies without leaving an estate. However, it is mustahabb that an heir perform Hajj on his behalf. This is the position of the Shafi`i, Hanbali, and Zahiri schools. It is the position of a group of the Salaf. This is the chosen position of al-Shinqiti and Ibn Baz.