Answer
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
Once a person has performed the standing at Arafah, he may delegate someone to do the tawaf Al-Ifadah on his behalf if he is bed-ridden.
In responding to your question, Sheikh Ahmad Kutty, a senior lecturer and Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states:
Ideally, each pilgrim ought to perform the essential rituals of hajj such as tawaf, sa`i, and standing at in Arafah himself. In the case of tawaf, if he not able to do so, he may use the service available.
Therefore, the question would only arise, if a person suddenly becomes ill, and thus prevented from doing it even with such services. In such a case, someone else can do it on his or her behalf.
That applies only to those who have performed the ritual of standing in the plains of Arafah. If, however, he has missed the standing at Arafah, then he ought to do the hajj another year.
Once a person has performed the standing at Arafah, he may delegate someone to do the Tawaf Al-Ifadah on his behalf if he is bed-ridden.
Almighty Allah knows best.