Your fault,you pay (insurance)
This is not a definitive answer, but after an incident at a previous school where I worked, the student who was at fault agreed to pay the insurance excess.
I wasn't involved in discussions about this, so I don't know whether he volunteered to do that or was asked to do it by the school (he certainly didn't begrudge it, he admitted responsibility, and came back to fly our aircraft again afterwards). I doubt there'd be a way the school could insist on a student paying anything unless it was agreed in writing in advance.
But pay the whole cost? No - the school's insurance should cover that. That's what it's for.