Commentaire sur La Genèse 23:3

מעל פני מתו, From before his dead one. It is assumed that the "dead one" was aware of what went on around her as long as the lid had not been put on the casket or equivalent (compare Shabbat 152). This also teaches that the dead is to lie on his back (Baba Batra 74).

ויקם אברהם מעל פני מתו, in order to attend to the funeral arrangements for the body of Sarah. The reason why the Torah added the word מתו, “his dead,” seeing we all know that Sarah had been his wife, i.e. “his dead,” is that this is an apt description for the body of the deceased person, such as מתי, “my dead,” in verse 4, or מתך, “your dead,” in verse 6.

מעל פני מתו, וידבר אל בני חת. As long as he had not buried Sarah he was not yet a mourner in the technical meaning of the word. He was therefore able to leave his house and assemble the people of the town.