Praise be to Allah.
If she cannot fast because she is sick, but there is the hope that she will recover and become able to fast later on, then she has to make up the days that she did not fast in Ramadaan, because Allaah says (interpretation of the meaning):
“and whoever is ill or on a journey, the same number [of days which one did not observe Sawm (fasts) must be made up] from other days”
But if she cannot fast and there is no hope that she will be able to do so in the future because of sickness or old age, then she does not have to fast, but she has to feed one poor person for each day.
The evidence for that is the report narrated by Abu Dawood (2318) from Ibn ‘Abbaas concerning the verse (interpretation of the meaning):
“And as for those who can fast with difficulty, (e.g. an old man), they have (a choice either to fast or) to feed a Miskeen (poor person) (for every day)”
[Ibn ‘Abbaas] said: This was a concession granted to old men and women who are able to fast but with difficulty, they have the option of not fasting and feeding one poor person for each day instead. Al-Nawawi said: Its isnaad is hasan.
Al-Nawawi said in al-Majmoo’ (6/262):
Al-Shaafa’i and our companions said: an old man who is able to fast but it is very difficult for him, and a sick person who has no hope of recovery do not have to fast, and there is no scholarly difference of opinion on this matter. Ibn al-Mundhir narrated that there was consensus on this point. But they have to give the fidyah (ransom, payment in lieu) according to the more sound of the two scholarly opinions.
Shaykh Ibn Baaz was asked in Majmoo’ al-Fataawa (15/203) about an old woman who is unable to fast – what should she do?
She has to feed one poor person for each day, giving half a saa’ of the local staple food, whether it is dates, rice or something else. This is equivalent to approximately one and a half kilograms. This was the fatwa of a number of the companions of the Prophet (peace and blessings of Allaah be upon him), including Ibn ‘Abbaas (may Allaah be pleased with him). If she is poor and cannot feed others then she does not have to do anything. It is permissible to give this kafaarah (expiation) to one or to more than one person at the beginning of the month, or in the middle or at the end. And Allaah is the Source of strength.
The Standing Committee (10/161) was asked about a woman who was elderly and unable to fast the month of Ramadaan. She has been in this situation of being too old and too sick to fast for three years. What should she do?
If the situation is as described, she has to feed one poor person for each day that she did not fast in Ramadaan in those three years, by giving half a saa’ of wheat, dates, rice, maize or whatever staple food you use to feed your families.