slough (n.1)

"muddy place," Old English sloh "soft, muddy ground," of uncertain origin. Compare Middle Low German sloch "muddy place," Middle High German sluoche "ditch." Figurative use (of moral sunkenness or Bunyan's "Slough of Despond," 1678) attested from mid-13c.

"to cast off" (as the skin of a snake or other animal), 1720, originally of diseased tissue, from Middle English noun slough "shed skin of a snake" (see slough (n.)). Related: Sloughed; sloughing.

"cast-off skin" (of a snake or other animal), early 14c., slughe, slouh, probably related to Old Saxon sluk "skin of a snake," Middle High German sluch "snakeskin, wine-skin," Middle Low German slu "husk, peel, skin," German Schlauch "wine-skin;" from Proto-Germanic *sluk-, of uncertain origin, perhaps from PIE root *sleug- "to glide."