I have a friend currently struggling hard with this. They know that going to the school for help is not an option for this exact reason. They are going to be looking out for the school first and the student second. That's really unfortunate because the school has everything in place to be able to help the most.
I'm at a loss for how to help, beyond just being there as much as possible. They are doing all they can to get better, seeing a psychiatrist, taking medications etc -- but they are still having suicidal thoughts on a daily basis.