Praise be to Allah.
If this sickness is not chronic and there is the possibility that she may recover from it, then she should wait until she recovers and then fast the days that she missed.
But if this sickness is chronic and there is no hope of recovery, then the obligation of making up those days is waived in her case, but she must feed one poor person for each day of Ramadan (that she did not fast).
Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) was asked about a man who lost consciousness every time he wanted to fast.
If fasting causes a sickness like this, then he should not fast and should make up those days later on. If this happens to him any time he fasts, and he is unable to fast, then he must feed one poor person for each day. And Allah knows best.
End quote from Majmoo‘ al-Fataawa (25/217).
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said:
The one who is unable to fast does not have to do so, because Allah, may He be exalted, says (interpretation of the meaning):
“and whoever is ill or on a journey, the same number (of days which one did not observe Saum (fasts) must be made up) from other days”
But after research and investigation, it becomes clear that those who are unable to fast fall into two categories: those who are temporarily unable to fast and those who are permanently unable to do so.
Those who are temporarily unable to fast are those who have the hope that what is preventing them from fasting will cease to affect them. This is what is mentioned in the verse. So the one who is temporarily unable to fast should wait until the thing that is preventing him from fasting ceases, then he should make up the fast, because Allah, may He be exalted, says: “the same number (of days which one did not observe Saum (fasts) must be made up) from other days.”
The one who is permanently unable to fast is the one for whom there is no hope that the thing that is preventing him from fasting will cease. He has to feed one poor person for each day that he does not fast.
End quote from ash-Sharh al-Mumti‘ (6/324-325)
With regard to what is meant by feeding the poor in expiation for not fasting: one poor person must be fed for each day that one does not fast. The amount to be given is half a saa‘ of the usual local staple food. This is approximately equivalent to one and a half kilograms.
It says in Fataawa al-Lajnah ad-Daa’imah, vol. 1 (10/167):
To pay the fidyah (penalty), it is sufficient for you to feed one poor person for each day that you did not fast. The rate is half a saa‘, which is approximately one and a half kilograms, of rice, wheat or similar staple food that is usually eaten in your country. End quote.
The food must be given to a poor person who cannot find sufficient food. Therefore, if there are no poor people in your country, it is permissible for you to delegate someone to give it on your behalf in a country where there are poor people. Allah has commanded us to do whatever we can.
For example, if in another country there is hardship and urgent need that is greater than in the country where you are living, it is permissible for you to send expiatory charity and other kinds of charity to it.
And Allah knows best.