ZDC ARTCC Controller reported Pilot crossed fix at RNAV published altitude instead of ATC assigned crossing altitude which resulted in ATC MSAW alert. Controller stated this is a common occurrence.

Narrative

Aircraft X was flying IFR from ZZZ to LWB. Upon checking on frequency I informed the pilots of the altimeter; ATIS code; and the expected approach into LWB. At around XA02; I turned Aircraft X left as a vector for the approach and informed them of an icing report about 15 minutes prior near the airport. After clearing them direct to HODFU; an initial approach fix for the RNAV Runway 22; I informed Aircraft X of their position relative to the fix. They were given an crossing restriction of 065 or above HODFU and cleared for the approach at XA06. This altitude complies with the MIA in that area north of the airport. Aircraft X read back the instructions correctly. At XA07; I observed Aircraft X descend to 062. I informed him to check his altitude and that he was 300 feet low. I repeated the crossing restriction. Aircraft X responded similar to 'Aircraft X Six thousand five hundred. Got it.'. Aircraft X descended to 052 before climbing back up to 065 then continuing the approach after HODFU. Recommendation: Any pilots unfamiliar with the airport or procedures should ask questions and pay close attention to detail when flying into airports near mountains. The approach chart also shows the bottom altitude for HODFU is lower than our MIA at the center level. I think this causes confusion with some pilots as they expect lower at HODFU than they are given and could lead to mistakes being made.