I am so sorry for your loss. I have never heard of a chicken able to survive, get food and water, with only one leg. While they make artificial leg for dogs, I have never heard it done for chickens. I am afraid you will save her suffering if you euthanize her.
we did euthanize her. not sure what got her. there was a break in the chicken wire above them. maybe a possum? she was three months old, in a separate pen. in our big coop, something carried away one of our big hens too.