He walks on, doesn't look back
He walks away, giving her no sign or help. The old-looking demon woman looks down at the muddy ground she is sitting on, but instead of crying and feeling bad for herself, she smiles. He does not see this because his back is to her. Her leg begins to heal, and her torn clothes become pretty. Her wet hair becomes dry and long, and her old look fades away, and her beauty breaks out. She was not hurt, nor old.
She was doing as an old demon friend once asked her to do. She had watched Sesshomaru for a long time. She had hope when he had saved Rin and even smiled when she saw he had saved a human Miko from the future. But even with all that, he was still cold and alone. But this old friend of hers asked a favor, knowing this was something he could not teach, for he had tried.
Her old friend just happened to be his father, and his father died knowing his son would not change completely. He gave Sesshomaru the sword of life knowing he would not misuse it, but he also gave it to him to teach him compassion. But one thing he knew he could not teach Sesshomaru was love. He knew his eldest son had one thing on his mind, power. So before he died, he asked a demon girl for help, a demon girl he knew could help. He wanted love for his son, it was the one thing Sesshomaru was lacking. He had everything else.
"Wait!" She calls out, her voice no longer in pain or old.