Tartar buildup infects the gums, erodes the bone, and sends bacteria into the bloodstream, which then settle on the heart valves. Obviously, it also causes pain, and sometimes makes it difficult or impossible for the dog to eat, and when bad enough even makes it hard for them to breathe. Cleaning the teeth also sends bacteria into the bloodstream; a vet would give antibiotics. If the tartar is that bad, he undoubtedly has teeth that need to be removed. Again, antibiotics are needed. I'm sure your grandma loves her dog. That being said, it sounds like the dog is suffering in multiple ways; ways that won't get better. Veterinary fees for the dental work might be more than she can spend. My suggestion: a quick trip to the vet. Vet MUST think it's YOUR dog. Ask them not to shave the injection area, and to humanely put the dog down. Arrange him in his bed in a natural & peaceful position, and "find" him. You can release the little guy from pain, and from a slow & painful death. Grandma will be spared the guilt of seeing him decline and not being able to afford to help him. Most people believe the fable that "died in his sleep" means there was no suffering...but that's only true with euthanasia. I know this is hard to do, but it's the kindest thing you could do for both of them.