It is not permissible for anyone to inherit from one who is still known to be alive, even if he is sick and has lost his memory, or is no longer accountable because of old age or senility or loss of memory or physical weakness. Rather this is the case even with regard to terminal illness, because one of the conditions of inheritance that are agreed upon among the scholars is that the person should have died, either in a real sense or according to a legal ruling, as in the case of a person who is missing and of whom no news is heard, or by assumption, as in the case of a foetus whose mother is beaten to death, so that foetus inherits from the blood money on the assumption that he was alive [when his mother died], then it is assumed that he died so that his share of the blood money can be inherited from him.
In al-Mawsoo’ah al-Fiqhiyyah (2/33) it says:
There are three conditions for inheritance:
1.That the death of the person be established, or he be regarded as dead on the basis of a ruling, such as a missing person if the judge rules that he has died, or on the basis of assumption, as in the case of the foetus who was separated from his mother by a criminal act, which requires giving a slave as diyah or blood money.
2.That the heir be proven to be alive in a real sense after the death of the person, or on the basis of assumption, like a foetus who came out alive in a stable manner for a time that shows that he was alive when the mother died, even if it (the foetus) was very small.
3.That it be known who is entitled to the inheritance, such as spouses, relatives or freed slaves; how they are related (to the deceased), such as whether they are children, fathers, mothers, siblings or paternal uncles; and the degree of relationship that connects the deceased to the heir.
Shaykh Muhammad ibn Saalih al-‘Uthaymeen (may Allaah have mercy on him) said:
As for the fact that the one whose estate is to be inherited should have died, that is because of the words of Allaah (interpretation of the meaning): “If it is a man that dies leaving a sister, but no child, she shall have half the inheritance” [al-Nisa’ 4:176]. What is referred to here is death, and leaving behind his wealth cannot happen except by his moving from this world to the Hereafter.
Death is ascertained by observation, or when it becomes common knowledge, or when two witnesses of good character testify to that.
With regard to death on the basis of a legal ruling, this applies in the case of one who has gone missing, if the period determined for looking for him has ended; in that case the rule is that he has died on the basis of what may be the case, meaning that the possibility that he has died is to be regarded as if it is certain when it is not possible to be certain, because of the actions of the Sahaabah (may Allaah be pleased with them).
Tasheel al-Faraa’id, p. 18, 19
Based on that:
It is not permissible to divide the wealth of a man who has been affected with Alzheimer's or any other kind of sickness, so long as he is still alive.
Moreover, we should point out two related matters:
1.It is possible that Allaah may decree healing for this sick person.
2.It is possible that one of the heirs may die before the sick person does, and if one of the heirs dies before the person from whom he would inherit, then his share of the estate dies with him; if he has taken his inheritance from that person whilst the latter is still alive, then he will have taken wealth that is not permissible for him.
And Allaah knows best.