Fiqh-us-Sunnah Volume 4, Funerals and Dhikr, Fiqh 4.063B.

The majority of jurists dislike the idea of placing a garment, a pillow, or the like for the deceased in the grave. Ibn Hazm, however, sees nothing wrong in placing a piece of garment under the body in the grave, in light of a hadith reported by Muslim from Ibn ‘Abbas who said: “A red piece of cloth was placed in the grave of the Prophet, peace be upon him.” Ibn Hazm says apparently it was Allah’s Will to permit them to do so, because His Prophet, the innocent and guiltless, and others who practiced it were, according to the consensus, indeed the best of men, and none of them ever objected to it.”

The scholars consider it desirable, however, for the head of the deceased to be placed on a brick, a stone, or on the ground with his right cheek on a brick or some other similar thing, and with his shroud removed from his face so that his left cheek is open to the soil. ‘Umar advised his heirs: “After having placed my body in the grave, leave my cheek open to the soil.” Similarly Ad-Dahak in his will gave instructions that his shroud should be untied and his cheek exposed. It is preferred if something, some bricks or stones or soil, is placed to support the body so as not to leave it flat on its back.

Abu Hanifah, Malik, and Ahmad hold that a piece of cloth may be spread over a female body, but not over a male body, when lowering it into the grave. The Shafi’i school, however, is of the opinion that doing so is desirable for both male and female.