Air Traffic Controller reported aircraft turning and descending off the instrument procedure resulted in flight towards terrain. Aircraft rejoined the approach procedure and landed safely at the airport.

Narrative

Aircraft was cleared for RNAV XX at ZZZ and to cross ZZZZZ at or above 9000. After ZZZZZ; rather than flying to ZZZZZ1 per the procedure; the aircraft went straight to ZZZZZ2 the FAF and chose their own arbitrary altitude to descend to. Part of this off route excursion was in a 7000 MIA (Minimum IFR Altitude) and part of it was in a 5600 MIA. I noticed the deviation and since the aircraft was already speaking with ZZZ radio; I had my trainee call radio immediately. I queried what the aircraft was doing and if they had cancelled/were on a visual approach. I heard the pilot reply no they were direct ZZZZZ2 to rejoin. Due to a combination of beautiful weather; proximity to rejoining the approach course; and the descent profile reference known terrain/obstructions I elected not to give a low altitude alert and monitored the aircraft rejoining the approach safely. Between ZZZZZ and ZZZZZ2 the aircraft descended from 9000 to approximately 3300. I requested ZZZ radio to advise the pilot of a deviation and had them call ZZZ [Center].Suggestion: Expect unfamiliar pilots in unfamiliar aircraft to do unexpected things.