The medical term describing the reddish-purple color that develops after death in the undermost parts of the body is

Livor mortis refers to the bluish-purple discoloration (lividity) under the skin of the lower body parts due to gravitation of blood after death. Vibices: pale marks caused by pressure (e.g. from a rope in hanging death or generally from tight clothing, e.g., socks, belt, and bra)
Tardieu spots: dark pinpoint spots develop in dependent areas (e.g., in the legs of a hanged person due to increased gravitational pressure)
Features of decomposition
Venous patterning (marbling): prominent purple discoloration of subdermal vessels
Degloving: Thermal exposure, immersions, or advanced decomposition of skin and tissues result in degloving of skin (common in hands and feet).
Multisystemic processes : mummification, putrefaction