TRACON Controller reported an aircraft descended below their assigned altitude resulting in the aircraft flying towards terrain. ATC canceled the approach clearance; climbed and vectored the aircraft back to the final approach course and they landed safely at their destination.

Narrative

Aircraft X was inbound from the west given vectors to final for the ILS at ZZZ. The pilots kept asking for lower. Controller had them at an appropriate altitude for the area they were in. As they were vectored on to final the aircraft started descending below the assigned altitude and eventually went down to 010 MSL about 8-9 mile final before the approach clearance was cancelled. Pilot insisted on continuing but upon further examination aircraft was also left of course and vectored to the east for another attempt. Readback all seemed clear; there was a possible language barrier as well with some accent on the pilots part. This all came less than 2 hours after receiving simulator training on Low altitude alert phraseology for both Controllers. Aircraft X was eventually re-sequenced without further issue into ZZZ. Pilot also asked for the weather information which was not available due to the constant issue of not having the weather populate correctly on the system; ZZZ is also not an adapted weather site in the system. ZZZ1 weather was issued to the pilots. Recommendation: No changes. the refresher training I do believe helped although the phraseology not issued properly. made the Controller aware of the possibility of the aircraft descending below a given altitude. Honestly; perfect timing of the simulator training!