Tom has a nine year old cat named Simon, and Simon has a claw problem. Tom writes:
Tom, the claws you noticed are no longer shedding their outer sheaths. As a cat's claws grow, they get replaced from the inside out. The dull outer sheath is shed to be replaced by the razor sharp claw underneath. This is a continuous process that's helped along by your cat's clawing behavior. That's right, they aren't clawing things to get back at you. Cats claw things to clean their claws and help shed these sheaths.
it's not unusual for older cats to develop the thick claw problem. As cats age, their claws grow more rapidly than before and they're harder to shed. Problems begin when claws aren't trimmed often enough or the cat doesn't use an adequate scratching surface often enough. So right there, you have two things you can do to help. Trim Simon's nails, including the thicker ones, frequently and make sure he has plenty of scratching surfaces that he likes.
Trimming a cat's claws can be a challenge, but it will be easier if you link pleasant things like treats to the experience. Always offer your cat a treat after you've successfully trimmed at least one claw. You may have to take it one claw at a time, but don't give up. Hold the cat securely and grasp the paw between your thumb and forefinger. Press gently and you'll extend the claw. Be very careful with a struggling cat because you don't want to accidentally cut too much. Never cut into the quick, which in most cat's claws is the clearly visible pink area. Only trim the tips. Most cats will take care of their back claws on their own, so you need only trim the claws on their front paws.
If you're trimming thicker nails, like the ones you described, Tom, you can also try to help Simon shed those extra sheaths, but be careful. His nail bed is likely very sensitive due to the unshed sheaths pressing into it. Just extending his claw between your fingers could create a lot of pain. If you can take care of the chore yourself, do so quickly and reward Simon for his patience.
In addition to regular trimmings, all cats need one vertical scratching surface that's at least twice their shoulder height and one good horizontal scratcher. These can be covered with any material, but they'll need to be rough to attract cats to them. Imagine the kinds of surfaces cats would encounter in the wild. The closer the scratching surface is to tree bark, the better, and the greater the likelihood that the scratcher will get used. Corrugated cardboard, sisal, and berber carpet are all popular options. Avoid posts covered in soft carpet. These appeal more to humans than they do to cats.
So, let's assume that Simon's nails have been adequately trimmed and he has scratching posts that he uses regularly. Now what? If Simon is no longer showing signs of pain, it would be best just to keep those larger nails trimmed up. If he's showing you that he still has some pain associated with his claws, it's time to take him to the vet. If there's any indication at all that a claw might have become ingrown, your veterinarian should be your first option.