Nothing to be alarmed at. Cat claws are sheathed and the sheaths do get “sloughed” off. Where’s the connection to the scratch post? Give it enough time, and you’ll most likely find a treasure trove of them around the base and vicinity of your scratchpost, especially if you have a brood.
Cats do not scratch furniture with malicious intent. It is part of their regular self-maintenance program to keep their claws nice and sharp for self defense. When cats scratch, they are actually dislodging and removing a transparent sheath that grows over the claws. You may occasionally find these sheaths buried in your carpet. Scratching also stretches and tones your cat’s back and shoulder muscles. Yelling at your cat or getting mad at him only confuses him, because he is doing what comes naturally, with the nearest tool at hand, which may presently be your prized Louis IVX chair you inherited from Aunt Blanche.
See the importance of having a scratchpost, and not just any scratchpost, but one that your cat is happy to use?
In addition to the scratchpost, it is important to give a clip in time. Clip on the claws that is. Here’s a great how-to, with pictures.
(Model: Philly. No cats, claws, or sheaths were harmed.)