Ungrounded system will not need a terminal for an incoming neutral but will still need a grounding electrode system and all non current carrying metallic parts of the system including raceways, boxes, etc connected together via equipment grounding conductors just like a grounded system does. The ungrounded system does require ground fault detection system - once there is a fault the system still operates but is now grounded through that fault. If there would be a second fault on another phase it will be no different from when this happens on a grounded system. The whole idea of an ungrounded system is to allow for orderly shutdown instead of immediate shutdown when a ground fault occurs where there is a process that may possibly have catastrophic results if it is not shut down in an orderly manner.