Sheikh Salman al-Oadah
A person who is sick, on a journey, or otherwise excuse from making a fast on time can break his or her fast and will have to make up the number of days that he or she has missed.
Allah says: “And whoever is sick or upon a journey, then (he shall fast) a (like) number of other days.” [Sûrah al-Baqarah: 185]
The days can be made up together or at different times, before the following Ramadan or afterwards.
If a person delays making it up the missed fasts for more than a year until after another Ramadan has passed, some of the Pious Predecessors were of the opinion that the person has to feed a poor person for each day as expiation for the delay, in addition to making up those fasts.
However, this expiation is not established by the Qur’ân or the Sunnah. What we have is the verse stated above. Therefore, the default assumption is that it is not obligatory to feed the poor, even if the person delays making up the fast until after the following Ramadan.
And Allah knows best.
Source: Islam Today