Praise be to Allah.
If a person is sick and unable to fast, one of the following two scenarios must apply: either his sickness is temporary, so he is allowed not to fast and he has to make up the fast after he recovers and becomes able to fast, or his sickness is chronic, in which case he is allowed not to fast but he must feed one poor person for each day.
See the answer to question no. 37761.
Fasting can only be done during the day, from dawn until sunset. The night is not the time for fasting. Allaah says (interpretation of the meaning):
“It is made lawful for you to have sexual relations with your wives on the night of As‑Sawm (the fasts). They are Libaas [i.e. body-cover, or screen, or Sakan (i.e. you enjoy the pleasure of living with them —)] for you and you are the same for them. Allaah knows that you used to deceive yourselves, so He turned to you (accepted your repentance) and forgave you. So now have sexual relations with them and seek that which Allaah has ordained for you (offspring), and eat and drink until the white thread (light) of dawn appears to you distinct from the black thread (darkness of night), then complete your Sawm (fast) till the nightfall”
This verse describes the time for fasting – which is the day – and the time for breaking the fast – which is the night. It is not valid, under any circumstances, to make the nights of Ramadaan the time for fasting.
It is proven that the Prophet (peace and blessings of Allaah be upon him) forbade continuous fasting. This was narrated by al-Bukhaari (1062) and Muslim (1102).
Continuous fasting means not breaking the fast at night and continuing to fast night and day.
Imam al-Bukhaari (may Allaah have mercy on him) said: “Chapter on continuous fasting and those who say that there is no fasting at night because of the words of Allaah, ‘then complete your Sawm (fast) till the nightfall’ and the Prophet’s prohibition of that as a mercy to them and to avoid hardship for them.
The basic principle with regard to physical acts of worship is that the Muslim should do them on behalf of himself, and they cannot be done on behalf of others. It is not permissible for anyone to pray on behalf of anyone else, or to fast on behalf of anyone else, according to scholarly consensus. Rather Hajj and ‘Umrah may be performed on behalf of one who is unable to do them during his lifetime, as is stated in the saheeh texts.
Ibn ‘Abd al-Barr (may Allaah have mercy on him) said:
With regard to prayer, the scholarly consensus is that no one can pray on behalf of anyone else, whether it is an obligatory prayer or a Sunnah or naafil prayer, on behalf of one who is living or one who is dead. Similarly, fasting on behalf of one who is alive is not valid and cannot be done on behalf of anyone else. There is consensus on all of this and there is no difference of opinion.
But if a person has died and still owes some fasts, this is a matter concerning which the scholars, both ancient and modern, have differed. End quote.
Fasting must be done during the day, not at night. Fasting at night is not valid.
It is not valid for anyone to fast on behalf of a person who is sick. If there is the hope that the sick person will recover, then he has to make up the fasts after he gets better. If there is no hope of recovery, then he has to feed one poor person for each day.
And Allaah knows best.