Your poor baby must have had some rotten teeth! The good news is now that the rotten teeth are out, she probably feels much better. The infection that was associated with those teeth most likely sent bacteria through her blood stream which would have made her feel puny. And, studies show bacteria of the mouth favor going to the heart, damaging the valves and linking to the development of heart murmurs.
On to your question: older dogs, like older humans, can have loss of brain function with age. Chronic infection (from dental disease, for example) can also lead to lessening of mental powers. Decreased brain function leads to decreased body function, including the muscle of the tongue. Without the teeth to hold the tongue in the mouth, some dogs end up with their tongue constantly hanging out of their mouths. For some dogs, their tongue may hang out one side of their mouth all the time.
For example, if the tongue hangs to the left that means the left side of the tongue is stronger than the right. Which means the right side of the brain is stronger than the left. (Most nerves to the spine and brain switch sides.) It’s even possible your dog has had mini-strokes.
There are some thing you can try. Again, if the tongue is hanging to the left, tickle the left side of the face. And focus your petting on the left side of the body. This puts more stimulating input to the right side of the brain and hopefully brightens it’s function. Massage and/or veterinary spinal manipulation therapy (animal chiropractic) are two treatments that help.
Interestingly, Chinese medicine calls this Spleen Qi (pronounced chee) deficiency. The Chinese Spleen is in charge of muscle strength, as well as digestion. Qi equates to energy and strength for us Westerners. From a Chinese medicine perspective, strengthening the Spleen and building Qi may help your dog. Acupuncture is one way to treat Spleen Qi deficiency. Another way is to feed high quality whole foods as they both strengthen the Spleen and build Qi.
Dogs with healthy Spleen Qi do not hang their tongue out when all of their teeth are pulled.
Many integrative veterinarians are familiar with these techniques and can help with your dog’s recovery.