Under what conditions is fasting exempted for a sick person?
Dr Zakir Naik: The people who are ill, they are exempted. Allah says in the Quran in

Surah Baqarah ch. no. 2 verse no. 185 that

"If a person is ill and traveling he can make up his prescribed periods of day of fasting later on"

but that does not mean if a person is suffering from a headache or a stomachache or a cough he should not fast.

If a person can fast if he is sick, it becomes compulsory for him to fast. The only time he is exempted is if fasting becomes difficult due to his illness or if he fasts, his illness would be increased or his health would detoriate or its compulsory for him to take some medicine due to his illness then it becomes prohibited otherwise for small issues or for small reasons like cough, like cold, like headache, like stomachache fasting is compulsory.

And the reason Allah (swt) has exempted those people who are ill so Allah (swt) does not want to put a burden,

Allah says in the Quran in Surah Baqarah ch. no. 2 verse no. 195 that

"Do not make your own hands the cause of your own destruction"

If I am ill and if I know that fasting is going to cause loss for me, will detoriate my health it's like killing myself. So Allah says its prohibited. So if I know fasting will detoriate my health then it becomes prohibited.

Similarly Allah says in the Quran, in Surah Nisa ch. no. 4 verse no. 29 that

"Kill not yourselves for Allah (swt) is the most merciful"

So causing a loss or a damage to your own health, to yourself is prohibited in Islam. So this exemption is mainly for these people for whom it is difficult or it will detoriate the health not for small ailments.