All perfect praise be to Allah, The Lord of The Worlds; and may His blessings and peace be upon our Prophet Mohammad.
The Last Tawaf is an obligatory rite of Hajj that a pilgrim is required to perform in its proper manner because failing to do so entails slaughtering a sheep, as a Fidyah, to be divided among the poor of the Haram area. This is according to the majority of the Muslim jurists: The Hanafite, The Shafite, and The Hanbalite since the Prophet (PBUH) has commanded Muslims to perform this rite, and, in principle, a command indicates an obligation.
Ibn Abdeen (May Allah bless him) said: "If he left Me`kah without having performed the Last Tawaf, then he is obliged to go back and perform it in case he hasn`t passed the Meeqat. If he has, then he either slaughters a sheep or assumes a new Ihram for Umrah where he performs its Tawaf, then offers the Last Tawaf that he had missed, and he is considered absolved from the liability of delaying it. However, slaughtering a sheep is better as it is easier for him and more useful to the poor. [Ra`ad Al-Mohtar,vol.2/pp.523].
Al-Mirdawi (May Allah bless him), a Hanbalite jurist, said when he was listing the obligations of Hajj: "This (Farewell Tawaf) is the correct opinion of the Hanbalite school of thought and the accredited view of the majority of the fellow scholars." {Al-Insaaf, vol.4/pp.60}. It should be the last rite to be performed before leaving Me`kah.
However, if a pilgrim performed it, but didn`t leave Me`kah, then there are two situations:
1. If he fell behind for a valid excuse, such as preparing luggage, waiting for the bus, or securing food supplies, then there is no harm in that, even if it took a long period of time.
2. If he fell behind for no valid excuse related to travel, such as visiting a sick person, attending a funeral and the like, then he is obliged to re-perform the Last Tawaf, and if he doesn`t do so, then he is obliged to slaughter a sheep.
Al-Khateeb Ashirbini (May Allah bless him) said: "If he wanted to leave Me`kah after having performed the rites of Hajj, then he should offer the Last Tawaf and perform its two Rakhas. This is indicated by the narration of Bukhari after Anas who said that the Prophet (PBUH) offered the Last Tawaf after he had finished the Hajj rites. It was narrated that Ibn ‘Abbas said: “The people were going in all directions, and the Messenger of Allah (PBUH) said: "No one should depart until the last thing he does is (Tawaf around) the House." {Bukhari}. After performing the Last Tawaf, offering its two Rakhas, making the recommended Du`a (supplication) at al-Multazam (area between the corner of the Black Stone and the door of the Ka`bah), and drinking from the water of Zamzam, the pilgrim should leave Me`kah. Yet, if he remains in Me`kah for no need or for an excuse not related to travel, such as visiting relatives, visiting a sick person, or paying a debt, then he should re-perform the Last Tawaf.
However, if the pilgrim was occupied with performing the two Rakhas of the Last Tawaf or preparing luggage, or food supplies, or performed the Asir prayer as it was called for, then he doesn`t have to re-perform the Last Tawaf.
Moreover, the Last Tawaf is an obligation as indicated by the narration of Ibn Abbas who reported: "The people were commanded (by the Holy Prophet) to perform the last circumambulation round the House, but menstruating women were exempted." (Bukhari&Muslim). However, leaving the Last Tawaf entails slaughtering a sheep as is the case when leaving other obligations." {Moghni Al-Mohtaj, vol.2/vol.280}.
If you (questioner) haven't intentionally delayed the Last Tawaf, and were forced to stay for a full day in the hotel waiting for the Hajj campaign, then you are absolved from the liability, and the Last Tawaf that you have performed avails you, Insha`Allah. And Allah Knows Best.
