ARTCC Controller reported having an aircraft assigned an altitude that was below the MIA resulting in the aircraft flying towards terrain. The aircraft was climbed to a safe altitude.

Narrative

I had just come back from break and asked the controller if they wanted a break. They said yes. While I was previewing the position and the boards; I heard the controller giving a squawk code to an aircraft. I had not plugged in yet. When I was ready; I plugged in to the position as the controller I was relieving was mid clearance for Aircraft X. They gave the aircraft a clearance and shipped them I think all in one transmission. When they started the briefing; if I remember correctly; the data block for Aircraft X was in a /0 position so I didn't pay much attention to it at the time. After the briefing; I did not have any questions and assumed the position. After about a minute and scanning everything over again. I noticed that Aircraft X was at 040; and that was the aircraft the previous controller had given the clearance to and 040 was 2500 feet below the MIA. I called the supervisor over to show them what was going on; and I saw the aircraft start flashing MSAW inside Tucson approach airspace; and they started to climb. This is when Tucson approach called the supervisors desk to ask what had happened. .