One of my sons is a renal failure patient; he is on CAPD and can’t fast due to his treatment (4 time a day one liter liquid is drained and inserted in the abdomen. Another has a transplanted kidney, doctors ask him that if he has to fast he will have to drink more and more liquid at nighttime. He has to sleep at night and could not intake the liquid in the required quantity, moreover recently a problem in the transplanted kidney is observed and he is afraid that if he fasts and could not take the enough liquid, the kidney transplanted may get worse. Both are dependent on the parents, have no earning source. Whether the parents have to pay the Fidiya for both against their number of fasts, they left during the month of Ramadan.

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

Whoever is unable to fast the month of Ramadan, or even some of its days, because of an illness which is expected to be cured, he can break the fast, but he must make up the missed days when he is able to do so. Allah Says (what means): {…but if any of you is ill or on a journey, the same number (should be made up) from other days.} [Quran 2:184]
However, in the case when his illness is chronic and it is difficult to be cured in the future, then he is permitted to break the fast, but he must feed for each day one poor person, that is approximately 750 grams of staple food, or rice or wheat, or something else.

It is not obligatory for his parents or someone else to pay an expiation instead of him, because it is related to his personal obligation and not to someone else. But if they grant it to him, it will suffice and for sure, they will be rewarded for that.

Allah knows best.