, and thanks for your question.
The new nail coming in forces the old one to split down the middle. When cat's scratch on a scratching post this helps pull off the old nail, but there is a point often where one side of the nail has come free and the other is still attached, so looks like the nail has split. Is that how it looks? If so, it will eventually drop off. Usually around the bottom of a scratching post, you can see these nail fragments.
If the cat has caught a nail, say in a screen, and pulled it off prematurely, it's possible it may have damaged it and there may be some redness or some blood at base of nail. If it doesn't bother him to scratch on the post, it's not likely causing him any pain. Usually this type of injury is self-healing, but if it looks puffy and infected
, then take him to the vet.
Cats are pretty fastidious about their feet about washing them, and you might observe them chewing at their nails to get the old nail sheath off.