If you are referring to a trip or pilot solenoid valve which is used to send a control valve or some other final control element to its fail or safe position e.g. fail open or fail close then the solenoid should be energized to allow control or regulation of the final control element under normal operating conditions, in other words de-energized to trip. This allows what is termed fail safe operation meaning that if there is a faulty connection, damaged cable or blown fuse etc the solenoid will be de-energized and the process will be taken to a safe state as opposed to energized to trip which means that if a faulty connection etc exists and a trip signal is generated the solenoid will not be energized and therefore no trip will be effected meaning potential disaster due to unsafe operating conditions.
Healthy state or not is meaningless when discussing the operation of trip solenoids.
"While process is going on"?? Get your terminology right if you're working in or aspiring to be considered a professional in this field.