All perfect praise be to Allah the Lord of the Worlds. May Allah`s peace and blessings be upon our Prophet Mohammad and upon all his family and companions.

If the pilgrim passes away after having performed minor and major Tahallul- thrown the pebbles, made Tawaf and shaved or cut hair-then their Hajj is valid. However, it isn`t permissible to delegate someone to complete the remaining Hajj rituals on their behalf because these can be compensated for by slaughtering an animal.

However, if a pilgrim passes away before performing minor and major Tahallul or between them, Shafii scholars have disagreed about the permissibility of delegating someone to complete the rituals on their behalf. However, the reliable opinion is the new view of Imam Shafie which states that it isn`t permissible to delegate someone to complete the Hajj rituals on their behalf. This is by analogy to the impermissibility of completing the prayer or the fast of someone who dies while performing these acts of worship. Consequently, the rituals that the pilgrim had performed are considered of no avail but he or she is rewarded for them. Moreover, if the pilgrim passed away without performing Hajj while it was required from them, the heirs should hire someone, from the inheritance, to perform Hajj on their behalf. However, if the pilgrim was doing voluntary Hajj, then delegating isn`t an obligation.

Imam An-Nawawi (May Allah have mercy on him) said: "If a pilgrim passes away while doing obligatory Hajj, there are two famous views in this regard: The more correct view (New opinion) is that this isn`t permissible by analogy to the impermissibility of completing the prayer or the fast of the person who dies while performing these acts of worship. According to the old view of Imam Shafie, this is permissible because it is permissible to delegate someone to perform Hajj on behalf of someone else. According to the new opinion, the acts of Hajj, which the pilgrim had already performed, are of no avail, but he or she is rewarded for them. In addition, the pilgrim who passed away without performing Hajj while it was required from them, the heirs should hire someone, from the inheritance, to perform Hajj on their behalf. However, if it is voluntary Hajj or he wasn`t able to perform it except this year, then Hajj isn`t obligatory. This is in case the pilgrim passed away before performing minor and major Tahallul since passing away after them makes delegating impermissible, and there is no disagreement amongst the Sahfie scholars about this view because it is permissible to compensate for the rest of the rituals by slaughtering an animal." {Al-Majmou` Shareh Al-Mohazab, Vol.7:P.135}.

Nevertheless, if the pilgrim became terminally ill during Hajj, but was able to continue while riding  vehicle or being carried, then he/she must complete the rituals because he/she isn`t excused not to do so.

If he couldn`t complete the Hajj rituals himself, such that he couldn`t perform some of the obligations (Throwing the pebbles) then he is cleared from liability because these can be compensated for by slaughtering an animal. However, if he failed to perform some pillars of the Hajj, then we have two differentiate between two situations:

First: If he entered into the state of Ihram on condition that he would abandon it when Allah would detain him, then he can abandon it by making the intention and shaving or cutting his hair, but he has to make another Hajj. The proof of this is that Narrated `Aisha: Allah's Messenger (PBUH) entered upon Dubaa bint Az-Zubair and said to her, "Do you have a desire to perform the Hajj?" She replied, "By Allah, I feel sick." He said to her, "Intend to perform Hajj and stipulate something by saying, 'O Allah, I will finish my Ihram at any place where You stop me (i.e. I am unable to go further)." {Bukhari & Muslim}.

Or, he said that if he got ill then he is free from the state of Ihram, then he is free from it without making the intention or shaving or cutting his hair, but he has to make another Hajj. This is because it was narrated from Ikramah, from Al-Hajja bin Amr that the Prophet said: "Whoever breaks his leg or suffers a leg injury, then he has exited Ihram, but he has to perform another Hajj." {Transmitted by Abu Dawoud}.

Second: If he didn`t enter into the state of Ihram on condition that he would abandon it when Allah would detain him, then he has to wait for what stopped him from completing the rituals to go away. If it is gone and the time of Hajj has passed, then he should perform Omrah, but he has to make another Hajj. For more details, check the book {Asna Al-Matalib Fi Shareh Rawd At-Talib, Vol.1:P.524}. And Allah the Almighty knows best.