Sheikh Muhammad b. Sâlih al-`Uthaymîn
Allah says: “Whoever is sick or on a journey should make up the number of days later. Allah wants ease for you, and He does not wish hardship upon you.”
Allah has made it obligatory upon the sick person to make up the days later. However, if he dies before he recovers, then he has dies before the time has come when the fasting of those days becomes obligatory on him.
With respect to those missed days, he is the same as a person who dies before Ramadan. No one has to feed the poor on his behalf on account of the coming Ramadan that has yet to arrive, even if he died right before the month of Ramadan began.
The same can be said for a sick person as long as he remains sick. He is not obligated to fast until after he gets better. Therefore, if he dies before he recovers, then he has died before fasting those days has become obligatory upon him. It is not obligatory for anyone to feed the poor on his behalf, since feeding the poor is a substitute for an obligatory fast. If the fast itself is not an obligation for him, then feeding likewise is not an obligation.
This is what the verse of the Qur’ân indicates – that if the person has not the ability to fast, then there is nothing upon him.
In the Sunnah, we have where `A’ishah relates that the Prophet (peace be upon him) said: “Whoever dies with a fast obligatory upon him, then his heir should fast on his behalf.” [Sahîh al-Bukhârî and Sahîh Muslim]
The ruling of this hadîth is clear. Its implication is that whoever dies without a fast being obligatory upon him does not have to have someone else fast in his stead.
As we have already explained, a person who is sick during Ramadan and remains too sick to fast up to the time of his death has no fast upon him.
And Allah knows best.
Source: Islam Today