Assalaamu alaykum. A relative is in their last stage of illness and has a few months to live. What can be read (from Quran) and done for them, and what could the patient do for themselves, as the patient is not a practising Muslim, and bearing in mind that they have no mobility. May Allaah reward you.

All perfect praise be to Allaah, The Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger. 

Scholars held different views regarding dedicating the rewards of Quran recitation and the like of righteous deeds to a living person. Some scholars maintained that it is permissible; the Hanbali book Mataalib Uli An-Nuha reads, “It is permissible for the Muslim to carry out a good deed with the intention of dedicating its reward or part of it to a Muslim person, dead or alive, and the reward reaches that person ... what matters in this regard is the doer's intention, and not the words used in dedicating the reward…”

Hence, there is no harm in doing that for your sick relative, and you have to remind him of Allaah and urge him to hope for Allaah's vast mercy and to perform righteous deeds within his ability in such circumstances. For instance, he may recite Thikr (expressions of remembrance of Allaah) and supplications, offer charity if he can afford it, listen to the Quran frequently if he cannot recite it himself, and do the like of the good deeds that he can carry out in such a condition.

It should be noted, though, that it is incumbent on him to perform the obligatory prayers. A Muslim is not exempted from prayer as long as he has a sound mind. A sick person who cannot stand for the prayer should offer his prayer while sitting, and if he cannot sit, then he should offer his prayers while lying down. If he cannot bow down or prostrate, he may nod or gesture instead. For more benefit, please refer to fataawa 84293 and 88501.   

Also, encourage him to have good expectations of Allaah for, verily, Allaah is as His slave expects of Him. Please, refer to fatwa 92083.

Lastly, we implore Allaah to grant us and your relative a good Khaatimah (final stage of life).

Allaah knows best.