Act how, if the social services and police are reluctant to meddle in family affairs (as seems to be the norm in the very conservative Japanese society)? Shelter her for a while? That'd just result in more beatings for her and a kidnapping case.
From what I can tell from a quick google search it's hard to move from your parents without legal consent from your guardian in Japan until you're 18. I think that usually you can when you're 16 in other Western countries, but I guess Japan is more strict about it. So basically parents own their children until they're 18 it seems.
Besides getting police and CPS on board, removing her from her mother to save her life and being sexually abused (or at least exploited for cp) would probably alleviate any charges, at least if the mother didn't want attention drawn to her. But it's really hard helping someone who doesn't want help and is locked into a mindset that they can't escape, having been manipulated and gas lighted since they were a child that they're not able to live on their own, that their life will be ruined if they tell, that they'll be killed or silenced and no one will believe them, that they're worthless and don't deserve help. The things she says to the guy is probably the same stuff her mother has told her over the years, and she's started believing it as a truth.
Honestly I've seen hard cases over the years, maybe not as severe as this but where it's obvious that the parents aren't good for the kids, but it'd probably be worse for the children to be put in foster care or an orphanage, and the children are so loyal and/or terrified of their parents that they can't deny them. You get the feeling that the kids just don't know any better. This haven't been physical abuse or sexual abuse though, but severe neglect and pretty harmful, and the kids usually suffer from mental issues and many of them start using drugs to cope. Even sadder when some start selling or using their body to get drugs from people exploiting them. It's sad to see self destruction like that, but it is what it is.
Sorry for the rant.