If Ramadaan comes and a person is unable to fast because he is elderly or sick with no hope of recovery, then he is not obliged to fast because he is unable to do so. So he should not fast and he should feed one poor person for each day.
Allaah says (interpretation of the meaning):
“O you who believe! Observing As-Sawm (the fasting) is prescribed for you as it was prescribed for those before you, that you may become Al-Muttaqoon (the pious).
184. [Observing Sawm (fasts)] for a fixed number of days, but if any of you is ill or on a journey, the same number (should be made up) from other days. 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). But whoever does good of his own accord, it is better for him. And that you fast is better for you if only you know”
al-Bukhaari (4505) narrated that Ibn ‘Abbaas said: This has not been abrogated. It refers to old men and old women who are not able to fast, so they should feed a poor person for each day.