Rabies is very uncommon in domesticated animals and unlikely to be the problem here. It is still a possibility since this cat has not been vaccinated. Drooling and lack of appetite signal nausea which can be related to many, many things. Have this cat examined by a veterinarian to rule out the common causes of nausea--like dietary indiscretion, diarrhea, intestinal parasites, pain (like from an abscess), foreign body obstruction, toxicity, kidney problems, or liver disease.
