Rotten Teeth itself doesn't cause death in a dog but when the dog has gum disease that leads to rotten teeth it can lead to heart disease and heart problems in the dog.
That heart disease and heart problems can lead to a heart attack in your dog which could cause death.
So if your dog has rotting teeth it's a good idea to take them to the vet to help fix the rotten teeth and clean their mouth of any bacteria that could cause more teeth to rot.
Once the dog has periodontal disease it can't be reversed but it's still a good idea to clean the dogs mouth and other teeth to get rid of any bacteria.