Generally, there shouldn't be any problems. It mainly depends on the extent and location of the fracture. If it's just the tip that's broken, usually no special treatment is needed; however, if the fracture is closer to the finger bone, you must receive anti-inflammatory treatment after bleeding, or go to the hospital for treatment. 
What to do if your cat's nail breaks and bleeds?
1. If your cat's nail is completely broken and bleeding, first disinfect the wound with alcohol, then apply styptic powder to stop the bleeding, and finally apply iodine solution and bandage it. Keep the bandaged wound dry. Have your cat wear an Elizabethan collar to prevent them from licking the wound and causing infection.
2. If the condition is serious, it is recommended to take the cat to a veterinary hospital for professional treatment.
3. During the wound healing period, the owner should not let the cat play in water. In order to recover as soon as possible, it is necessary to restrict the cat's behavior in a positive way.
4. You need to adjust its diet; a lighter diet will help the cat heal faster.
