A single circuit system is one in which trip components are placed in series. In a deenergize-to-trip design, a single component failure in this circuit causes the system to trip and shut down the equipment.
Another single circuit system is one in which energize-to-trip components are placed in parallel. If a single component fails in this circuit and that component becomes the trip initiator, nothing will happen. No action will occur; nor will that particular part of the shutdown system perform its protective function if called upon to do so by an abnormal operating condition. The facility could be unprotected.