Each state will differ a little on how they handle this situation, and even in the states the individual schools will differ some. The best thing is for him to go to them and tell them it was a mistake to drop out and he really wants to make it up. He needs to make them believe that he will come back at any cost and then convince them that there is a significant reason for allowing him to take classes this summer to allow him to finish his 10th grade courses. If he goes in saying that he will come back if they will let him move on, IMO, there is no way they will let that happen. Now I have nothing to do with education, but this is from experiences I went through when younger.
Possibly have him mention to them that he wants to get the rest of his education and get get to college. And he'd like not to have to suffer an entire year set back for a poor decision he made once. And don't get me wrong, I'm not saying it was a poor decision. I don't know the situation and getting a GED and then going to college or work is essentially the same thing in my book.
You really might want to talk to him about the GED thing b/c he can most likely get that done in less time than it would take him to complete the last 2 years of school. Anyhow...that's my .02...take it for what it is