In the event you have an elderly pet that you just cannot keep, my advice is to seek a home for the pet with a friendly family member, or someone the pet is familiar with. Check with your humane society or place an ad. Believe me, there are people would care for your pet. Over the years I have adopted many elderly pets and have found that they are loving companions. They may sometimes take longer to adjust to you and your family, but with lots of love, patience, and understanding they soon adapt to their new-found family.
Elderly pets are great for older persons or someone wanting a calmer pet.
I find many people cannot cope with a puppy or kitten or a younger pet. I only advise putting your pet humanely to sleep in extreme cases such as where she may be suffering from a severe medical problem or has become aggressive due to pain, etc. Elderly pets are like elderly people. They need to be wanted, loved and cared for. They need to live out their natural lives with dignity.