In every case, however, they must make up the missed fasts, because Allah, Exalted is He, has prescribed fasting for every Muslim. Regarding the sick person and the traveler, He says: “Then let them fast an equal number of days other than these.” [al-Baqarah 2:185] Although they break their fast with a valid excuse, making up the fasts is not waived for one who breaks it due to illness or travel; so it is even less likely to be waived for one who breaks it merely for relief.
As for feeding a needy person, there are three cases:
The first case: if they break their fast out of fear for themselves, they need only make up the missed fasts; that is, nothing further is required of them.
The second case: if they break their fast solely out of fear for their children, they must make up the missed fasts and feed one needy person for each day.
The requirement to make up the fasts is clear, since they broke their fasts. As for feeding a needy person, it is because they broke their fasts for the benefit of someone else, and thus feeding is required of them. Ibn Abbas, may Allah be pleased with him, said concerning the verse, “And upon those who are able to fast is a ransom: feeding a needy person” [al-Baqarah 2:184]: “It was a concession for the elderly man and the elderly woman who were able to fast: they could break their fast and feed one needy person for each day. Likewise, if the nursing woman and the pregnant woman feared for their children, they would break their fasts and feed a needy person.” Abu Dawud narrated it (1).
It was also narrated from Ibn Umar, may Allah be pleased with him (2).