Legal liability is when you expose yourself to a risk of very high damages in US of A. For example, you run a corporation, and if your business fails,, you lose your business, but not all your private property. If you start behaving illegally, say, comingling your own money with corporate, this opens a way to lose everything you and your family have. (this is an illustration, not a legal advice, I am not a lawyer).
Same here, yeshiva may lose all their funds and licenses to a lawsuit by someone hit by a drunk yeshiva-bocher. Presumably, yeshiva is making use of donations, and I can’t imagine how one can risk someone’s holy tzedoka in such a way.