Could governors find themselves liable for any financial commitments if the school runs out of money, and what about being sued by parents or staff?

There is no individual financial responsibility for governors. Any debt the school may run up would be discussed with the LEA and would probably have to be paid from the next year's budget. If however a governor acts fraudulently, s/he is liable to the normal processes of law. In the case of any claims for negligence, governing bodies are covered by corporate insurance cover arranged by the school or LEA.