Is there any way for his insurance to cover my loss and pay all the damages?

I was in the car with him and he lost control and smashed into a tree. I have liability only on my car and he has full coverage on his. I have been reading up and most laws say that if the damage exceeds the limits of my policy that it would then go to his policy. That usually is talking about damages caused to the other car or party that gets hit. Can this apply to my damage also? Also he is not poor but I am not sure he has enough to pay for everything I need to repair my car. Can the garnish wages or put him in debt? And if he lives with his parents still and on their insurance policy can they be held responsible? (They are very well off and that why I ask) I am not trying to rip someone off but I feel that I should have my car fixed considering he wrecked my car because he let off the clutch too quickly and lost control.