TRACON instructor reported an aircraft that was NORDO entering a higher elevation than it was assigned due to radio problems.

Narrative

Aircraft X was on the TMBRS arrival landing PDX expecting ILS runway 10L approach. Aircraft X was issued 030 altitude assignment at XA:35z. Pilot descended to 030. then at XA:38z Aircraft X was given a bases turn vector of heading 010. Pilot did not respond. We tried again. Nothing. Then we asked Aircraft X to ident. Nothing. The pilot is now close to entering higher terrain. We had all sectors in the TRACON; the last Center sector and our Tower try to reach the aircraft. No luck. Our radios were good due to other radio checks with other aircraft. Then when Aircraft X was about 4 miles from terrain shown on our EOVM map; the pilot checked on and asked if they missed anything. They switched frequencies on accident. We immediately turned aircraft toward the airport and climbed aircraft to safe altitude. I was instructing a trainee at the time and the Supervisor was not in the operation at the time as well. Nothing to recommend. Pilot error. The supervisor should have been in the room to help with all the coordination. Maybe a cell phone call; not sure that was in the remarks or not. We didn't have a strip.