Center Controller reported a NORDO aircraft that was below the MIA.

Narrative

Aircraft X departed BIL assigned 140 entered a 148 MIA (Minimum IFR Altitude) polygon about 10-15 miles outside of BIL approach airspace. Aircraft was NORDO with 15 and never talked to sector 15. As the aircraft approached 06 airspace the handoff was initiated and they were called; where they were able to contact him and give him a climb above the terrain. BIL approach began the handoff during some moderately busy traffic; another Controller opened the D-side during the handoff. I believe the D-side took the handoff; I do not believe I accepted the handoff but I cannot say for certain. When the aircraft was approaching 15 (approximately 10 miles before entering 15 airspace) airspace I looked at the altitude and route of flight; noticed the confliction with terrain and began attempts to reach/control the aircraft. Multiple attempts to contact the aircraft both through approach (mostly coordinated by D-side) through guard; through 15 freq and through an aircraft relay on 15 freq no responses. Low altitude alert was given in the blind. BIL Approach said he readback the first freq change and were not able to contact him after that. Easier/quicker ability to contact the pilot in these instances. Pilot paying closer attention to frequency changes and attempt to find the right frequency; given they were not talking to anyone.