WEAR GLOVES!!! The rabies virus does die pretty fast when dried, so old dry saliva is probably safe. Probably. The issue is when the pet is just involved with the possibly rabid critter, and the owner immediately rushes to handle the pet, fresh saliva and all. That's an exposure!
It's best to have a body to be tested the next day for rabies; wrap it in plastic and chill, don't freeze it. Animal Control where you live SHOULD pick it up and transport it to your state lab for testing. SHOULD, but it can be difficult. PERSIST, call your veterinarian, call public health, and insist.
If there's no body to be tested, but a likely exposure, you would be getting vaccinated.
Mary