Another song that was traditionally sung at a time like this by folks from the Ozarks (and elsewhere) is "Angel Band." The family would gather around the bed of the dying person and sing this song to gently usher them to their "immortal home." A very beautiful song, recorded by many.

"Angel Band" and "Won't You Come and Sing for Me" are both in the DT, although I use slightly different words for "Won't You Come...."