There was actually a Radiolab episode about this scenario. A kid grew up with insane parents and later joined the real world and was in a fucked up legal limbo status due to there being no record of their birth. They couldn’t prove they were even a natural citizen of the US. It’s been several years since I listened to that episode, but iirc their state senator/some politician ended up campaigning on their behalf to get laws made to cover these fringe cases so in the future, kids like these aren’t completely screwed. Not sure if the law ended up getting passed or not. Anyway, it was the first time I’d heard of people doing this kind of crap to their kids and it blew my mind. Utterly selfish and abusive.

Edit: found the episode: https://radiolab.org/podcast/invisible-girl