The Ruling on making Tayammum on a Carpet
Question :
A person was in the hospital and was unable to perform Wudhu', so he made Tayammum for prayer, but he did so on a carpet; is his prayer correct?
Answer:
It is required of a sick person to perform ablution for prayer, if he is able to do so. If he cannot, he must make Tayammum with earth which contains dust; if he unable to obtain it, he must make Tayammum against tiles, if there is dust on them, or on his mattress, if it has dust on it. If there is no dust on it, then he must make it on the nearest earth to him, or on the nearest earth possible, or what of it he can reach, based upon the Words of Allah, the Most High:
"So keep your duty to Allah and fear Him as much as you can".
and His Words:
No person shall have a burden laid on him greater than he can bear.
Source:
Ibn Jibreen
Fatawa Islamiyah, Vol. 2 Pages 58-59