Can’t she just put him up for adoption?
Who would even want to take him? ... and that seems to be the problem right now ... no one wants him! [ ... and for whatever reason they have ... ]
Appy, most foster parents don't have the skills for this and most states lack the common sense to do proper placements. A Foster Dad in my state ended up with an involuntary manslaughter conviction because DCS did an improper placement of a teen who had tried to strangle a previous foster mother.
The foster dad had to place the teen in a hold for his families protection until help arrived and the boy struggled so violently it killed him. DCS made the man their scapegoat. This involved a troubled teen with a history of mental issues and violence. DCS also did not inform the new FP of the danger. Even at that and with the judge chiding DCS he was still convicted. DCS made sure they placed the blame on the man.
No these kids at least until they can be stabilized belong in a secured professional inpatient care facility and then determine the actual level of care they need once there. As for cost? Most of the time it is out of the families reach. As for precedents in these extreme cases of state stepping in and funding such a facility it's well over 100 years old. The facilities are being closed right and left and the idiot Chest Thumping Morons who pushed to have them closed have not one single clue as to the disaster it has created.
There isn't really that high a number needing that level of care. These are extreme cases many times where child due to brain damaged during their forming in the womb or an illness has damaged their brain. As such they can not discern many needed attributes such as understanding right from wrong nor can they many times be taught. They will face an institutional life which is not near as cruel and insane as turning them loose on the streets or to family who doesn't have the means or skills to pay for or give themselves the necessary help.