All perfect praise be to Allah, The Lord of the Worlds. I testify that none is worthy of worship except Allah and that Muhammad is His slave and messenger.
It is obligatory for the one who was not able to fast Ramadan on account of sickness, travelling, or so on to make up the days he did not fast at any time he is able to fast throughout the year. If he is not able to make up for them until the next Ramadan comes, then he should make up for them after it and is not obliged to observe an expiation of feeding, and there is no sin on his part because he is not negligent. However, if he was able to make up for the missed fasts but did not do it until the next Ramadan came, then he is obliged to make up for the missed fasts and offer one poor person a mudd (two thirds of a kilogram) of food for each day as expiation. The feeding of the poor that your relative observed is not actually sufficient for making up for the missed fasts for the one whose inability to observe fast is ongoing. Therefore, the questioner should know that it is obligatory on the person who was sick in Ramadan and was unable to fast except in the next Ramadan to make up for the missed eight days, and he is not obliged to give food at all. The food that he gave is not actually sufficient for making up the missed fasts.
Allah Knows best.