Thanks for the additional information. It is helpful. As you may be aware of, a dog has certain enzymes in their bodily fluids like tears and saliva that can cause a chemical reaction on the hair turning it a reddish color and eventually a brownish color. However, when a dog licks even just a little, it can start the process and a skin dermatitis such as a yeast dermatitis might also lead to some staining of the coat and a darkening of the skin underneath the coat. So it will be helpful to determine if the skin under the coat is discolored as well.
If the skin is also discolored, you might try some selsun blue shampoo and let the lather sit on your dog's skin and coat for about 15 minutes so it has time to work on the yeast dermatitis then relather and rinse. This will help if a yeast dermatitis is present. For paws, you might want to use some miconazole cream (available at most pharmcies).
The website below has a different approach suggesting altering your dog's pH levels to prevent the staining which you may wish to look at.
There is also an antibiotic that your vet can prescribe called Tylan that has been shown to be useful to stop tears and saliva and other fluids from discoloring a dog’s coat. You will want to ask your vet about this.
Now female dogs can have leakage from the vulva or urethra and both sexes can have seepage from the anal glands which might also contribute to the discoloration. Now another common cause for the coat to start changing color is flea dirt or feces which is composed of mostly blood so that leads to discoloration. Fleas do like the area around the rear and the rear legs as it is hard for a dog to reach those areas to bite and scratch. If you take a white cloth that is damp and rub it over those areas, it should show up pinkish. If it does then it may very well be flea dirt and getting rid of the fleas will help solve the issue.
At your dog's age, her immune system is likely to be failing so skin infections are going to be an issue. While saliva, drool, and tears are often the cause for the area to be wet, puddles, rain and other sources of moisture could also lead to a yeast dermatitis and the discoloration.
Now if you do the rub test and find fleas are the problem, wash Tuffy in dawn dishwashing liquid leaving the lather on 15 minutes to kill the live fleas. Then get Tuffy on a different flea preventative and treat your home as well. Any flea spray with an insect growth regulator (igr) should work well to remove the fleas from the home.
I hope this information is helpful to you. If you would like any additional information or have more questions please don’t hesitate to press the reply to expert or continue conversation button so I can address any issues you still have . If you do find this helpful, please take this opportunity to rate my answer positively so I am compensated for my time.