@Abedeus The parents haven't filed any missing person reports, though, as far as I can deduce things, considering nobody's looking for her. So, Sayu isn't even officially missing. I don't know the laws and practices in Japan well enough (like at all) to imagine what would happen if her case somehow did become a police case. Maybe it would be taken on by some youth protection officials, who knows, or maybe the cops wanted to get rid of her as smoothly as possible and simply shipped her back to the parents, like you said.
I doubt Yoshida would get into legal trouble since Sayu isn't missing and nobody could prove he has done anything to her. He might lose his social standing, though, and get fired, that much would be easy to imagine.