Frankly I'm surprised there already isn't a mechanism for long-resident children to obtain legal status at their majority.
I guess I don't see an illegal getting at least 5 years of free education in America as an extreme case. Frankly they should be extremely lucky and grateful they got by with it for as long as they did. Ask for citizenship on day one of enrolling, and if the kid doesn't have proof, then they and their family are out of here.