Center Controller reported a helicopter; departing an airport; leveled off at an altitude below their assigned Minimum Enroute Altitude.

Narrative

Prior to me taking over the position; the previous controller briefed me that Aircraft X had been issued a departure clearance via the SID to climb to 8000 ft. through clearance delivery. I assumed the responsibility of the sector and at the clearance void time the Aircraft X flight checked in level at 4000 ft. I responded notifying the Aircraft X that they should be climbing to 8000 ft. considering what I was briefed. The aircraft had yet to be radar identified at this point. Bottom Line. Low altitude alert was not issued. The MEA in that area was 6000 ft.Clearances from the ZZZ airport should be done directly with the controller from the ground considering we have radio coverage all the way to the ground. There is no need for FSS or clearance delivery to be involved with issuing that airport departure clearances. Additionally; the aircraft commander should be aware of the requirements of a departure procedure. If the procedure requires you to climb to a higher altitude than what was ATC cleared (IE the ZZZ departure); then they should question the clearance before departing.