Opinions on putting dog down. Help needed!

Little back story… We took in a rescue that was severely injured on her back. Looked like a car or predator had removed a large portion of the hide on her back and exposed the flesh. We nursed her and brought her comfort, but the wound would never heal. It’s been a long battle of a little over four years. We’ve taken her to multiple vets and there aren’t any solutions. She is living in pain and we are continuously fighting infections to her wounds. It’s gotten to the point to where we are wondering if we are doing the right thing for the dog or if we should put her out of her misery. Her wounds have recently taken a turn for the worse and the infection has spread to normally healthy tissue. I came to this board because I know y’all would give the best advice in a bizarre situation. Anybody have a situation similar with a successful ending?

Thanks in advance