Yes, your cuticles can overgrow. It is possible that they could get too long, though this is not common. The most likely reason you would have overgrown cuticles is because of a fungal infection or psoriasis, both of which can cause thickened skin on your hands, including the nail bed. If you have any concerns about your cuticles growing abnormally, see a doctor to determine the cause and get treatment for it as needed.