We are inspired by those who move like cats on the mat, but no one should have claws like a cat when training jiu jitsu. Keeping your finger and toe nails short prevents you from scratching your training partners and you from injuring your fingernails while grip fighting. No one wants an open wound, so just like you shower after every class and wash your gi after every class, make sure you always keep your nails short.
Public service announcement aside, if you are constantly losing your pair of nail clippers, this is your solution. Keep your clippers with you at all times using the Nine Lives keychain, nail clipper, bottle opener and nail file combo available here.
Remember, just don't cut 'em too short, we all have been here: