Why wouldn't you want your adoption regulated? I've heard of people that adopted young russian kids even as toddlers the orphanages damaged them psychologically and adoptive parents couldn't handle them. I could see where that might be hard to find the right resources. Rehoming might be a way to sell a kid to god knows who. If there is no paperwork maybe they didn't want her as child. Is there proof she went to school do teachers remember her. This sounds like human trafficking.
I mean *i* would want my adoption regulated. So I don’t have answers to your questions but the link I posted has a few Q&A that gives insight into why people do it. Not saying they are good reasons.