Sloughing (pronounced "sluffing") in biology refers to the act of shedding or casting off dead tissue, such as cells of the endometrium, shed during menstruation, or the shedding of skin in amphibians.

Skin sloughing is the process of shedding dead surface cells from the skin.

(https://en.wikipedia.org/wiki/Sloughing)

When I moved to Utah, and heard people talking about "sloughing", I had no idea what they were talking about. It's a Utah-ism as far as I can tell.