ATC Center Controller reported IFR aircraft departed without an assigned SID which resulted in the aircraft flying towards terrain below the MIA for the area. The Center Controller climbed and vectored the aircraft away from the terrain.

Narrative

Aircraft X departed SAF runway 02 under IFR clearance. Flight plan route SF.V263.ZZZ..ZZZ; climbing to 100. the pilot checked in on the frequency saying they are flying runway heading. I asked the pilot to verify that they are flying runway heading; and not flying any form of departure procedure. Pilot verified; and I issued the climb initially to 110; then to 140. With the aircraft being high-performance jet; the pilot was able to avoid entering the next MIA block below the altitude; albeit barely. As soon as the aircraft left 110 I issued the vector to avoid the upcoming 140 block. The aircraft exited out of the high terrain; and was cleared on course to ZZZ. Suggestion: Although it is relatively rare occurrence; pilots seldom check in on frequency departing SAF flying runway heading. On the runways 33 and 20; it is often non-issue; and the course corrections can be made before any imminent situation. However; aircraft departing runway 02 flying runway heading causes imminent situation as the terrain climbs rapidly. In this instance; the aircraft in question was a very high-performance jet; and the communication was not an issue allowing the situation to be resolved. If the aircraft involved was a low-performance propeller driven; or the communication was an issue; the situation could have been fatal. The fact that this is a recurring issue; the way the aircraft are cleared from SAF ATCT has to address and emphasize how to join SID or to proceed on-course away from high terrain.