What kind of dog do you have? 16 years old is for a dog is equivalent to 112 years in human life. So your dog is already in his last leg. Just imagine a human being even at 100 years old, they don't have appetite to eat at times. I think you need to take this dog to the vet and tell him what's going on with him. Cleaning the teeth or teeth extraction could be expensive. Your dog could be possibly dying because he's too old. You need to decide if you will be able to cope seeing your dog not eating and also seeing him deteriorate which could not be avoided.
I understand how it is to see your pet suffer, after all they are a part of the family. I sympathize with you.
Take care.
