بسم الله الرحمن الرحيم
Question: Is it obligatory upon the person of old age and the one suffering from a chronic illness (those who are not able to fast) to feed poor people?
Answer: The scholars have differed regarding this matter. The Jumhūr (the majority of scholars) see the feeding of a poor person to be obligatory upon the one who is unable to fast. However, that which is correct is that it is Mustaḥabb (highly recommended) as there is no clear proof stating its obligation. As for the verse:
وَعَلَى الَّذِينَ يُطِيقُونَهُ فِدْيَةٌ طَعَامُ مِسْكِينٍ
“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 poor person (for every day)”
This was during the earlier stages of its (fasting’s) legislation. This verse was then abrogated  by the verse that follows it:
فَمَن شَهِدَ مِنكُمُ الشَّهْرَ فَلْيَصُمْهُ
“So whoever of you sights (the crescent on the first night of) the month (of Ramadān), he must observe Saum (fasts)”
Ibn Ḥazm rahimahullāh said: “Fasting is not obligatory upon the ill and old people who cannot fast (are not able).
Allāh the Most High said:
لَا يُكَلِّفُ اللَّهُ نَفْسًا إِلَّا وُسْعَهَا
“Allāh burdens not a person beyond his scope”
And if fasting is not obligatory upon them, then likewise expiation (in its place) is not obligatory, because Allāh did not oblige them to do so, nor did His Messenger salla llāhu’alayhi wasallam and the wealth of the believers is protected and impermissible (to be wasted or taken without right) except if a clear proof or consensus of the believers exists.” Al-Muhalla: 4/415
Taken from: Translation of “Rulings Regarding Fasting [Summarized]” by Abu ‘Abdillāh Mūsā al-Bur’āwī
 ‘Abdullāh bin ‘Abbās رضي اللّه عنـه said that: “This (āyah) has not been abrogated, and it applies to old men and old women who cannot fast, so for each day they should feed one poor person.” Narrated by al-Bukhāri, 4505