Praise be to Allah.
Firstly:
Tawaaf al-ifaadah is one of the pillars or essential parts of Hajj, and the pilgrim cannot exit the final stage of ihraam except by doing it. Based on that, your uncle is still in ihraam so several things are required in his case:
1 – He must refrain from intercourse until he has done tawaaf al-ifaadah and exited the final stage of ihraam. If he had intercourse when he did not know that he was still in ihraam, he does not have to do anything, but he must refrain from intercourse from now on.
2 – He must go to Makkah and do tawaaf al-ifaadah. It is mustahabb to go to Makkah for ‘umrah, then when he has finished ‘umrah and shortened his hair, he should do tawaaf al-ifaadah. This is so that he will not enter Makkah without ihraam.
See: Majmoo’ Fataawa Ibn ‘Uthaymeen (23/194).
3 – With regard to tawaaf al-wadaa’, if he does tawaaf al-ifaadah and leaves Makkah immediately after that, this tawaaf will suffice for both tawaaf al-ifaadah and tawaaf al-wadaa’.
Secondly:
It is not permissible for him to appoint someone to do tawaaf on his behalf, because tawaaf is a pillar of Hajj and is not a matter for which one can appoint a deputy.
But if he is unable to go to Makkah, because of sickness or because he is financially unable, then some of the scholars regard him as coming under the same heading as one who is prevented from proceeding with Hajj. So he should slaughter a sheep where he is and distribute its meat to the poor and needy. Thus he will exit ihraam and will not have to do anything more after that. But if this was the obligatory Hajj of Islam, then he still has to do it, because this Hajj was not completed. Whenever he becomes able to do Hajj, it is obligatory for him.
Al-Ramli said in his commentary on Asna al-Mataalib (1/527): From the concept of the one who is prevented from proceeding with Hajj, al-Buqayli deduced that if a menstruating woman did not do tawaaf al-ifaadah, and she could not stay there until she becomes pure, and she went back to her homeland when she was still in ihraam and did not have any money and could not go back to the Ka’bah, then she is like one who has been prevented from proceeding with Hajj, so she should exit ihraam by means of making the intention, offering a sacrifice and cutting her hair. End quote.
Something similar is said in Mughni al-Muhtaaj (2/314) and Nihaayat al-Muhtaaj (3/317).
And Allaah knows best.
Comment