Conclusion
Billy was not even the boy's real first name. The authorities ran a fingerprint check, and a check on missing persons, but found nothing that fit the boy's description.
They surmised that his parents had not reported him missing, something many parents do, when they are ashamed for the neighbors to find out what has happened.
Since Billy, as he called himself, did very well in therapy, he was sent to a foster home where he could live a much more normal life than he could have in a detention center.