A pilgrim died in 'Arafah, so is the Hajj completed on his behalf, or is Hajj performed on his behalf?

He is not to be حج for, because he has fulfilled his obligation. The Prophet, peace and blessings be upon him, did not command to complete the Hajj for the one whose she-camel threw him off at Arafat. Rather, he commanded that he be washed and shrouded without embalming or covering his head, because he will be resurrected proclaiming the talbiyah.