We have a bug here in Arizona, a big black beetle, that likes to nibble on the new growth of cacti. I would suspect some similar insect. It apparently likes the tender flesh more than the skin. The white shells look like the cacti's skin after the bug has eaten the pulp. It's leaving it behind like the rind of a melon. I would treat it promptly with some type of deterrent like Cayenne or Tobasco. Fortunately the adult beetles are only around for a little while to mate and then die. The damage is permanent but the plant usually survives.
I recently bought a pot with 9 cactus in it (planning on separating them into individual pots) and the one you show was one of them. A week or so later that plant was eaten down about 1/4 the way, although I don't remember seeing such thin casings left. The other plants which all had thorns were fine, but I did see the tell tale slime trail across their thorns so I'm assuming it was snails or slugs. I moved the pot to a place difficult for them to get to and they haven't disturbed it since, but hopefully slithering across the other thorns poked them to death.