[Reg]

Hello:
I was just having a good look at the photos and my thoughts would be to check out the possibility of "nail fungus". It's quite common in cats and dogs.
If it's caught early enough, it's fairly easy to treat with an anti fungal agent or an anti bacterial agent.
I think if I were you, I would be seeking professional assistance either from a vet or a groomer.
Keep us posted.
You need to provide pictures of the other end of the cat, please.