Doorway carpet damaged by ferrets...any suggestions?

My furry children do not like being denied access to certain rooms, and as a result have damaged the carpet beneath a few doors. I'm not interested in laying more tile or in replacing the carpets at this point. I'm looking for a solution that will cover the damage that has been done and not look horrible. A few of the doors have carpet on one side and ceramic tile on the other, one has carpet on both sides. Is there a transition piece (not sure what they're called) that would be wide enough to cover the damage (about 4" at the widest)? If anyone else has had this problem, I would appreciate any ideas! Thanks! :)