Pilot reported while taxiing across the runway at a non-towered airport; after landing traffic; another non-communicating aircraft entered the runway and proceeded to takeoff; passing 200 feet overhead the reporter's aircraft.

Narrative

We were holding short of the runway on the east side at A2. A aircraft was on short final for a full stop and so we held short. After landing; the aircraft slowed and started to turn off the runway; We made a radio call and crossed the runway. Without calling; Aircraft Y entered the runway behind the landing plane and proceeded to take off whilst we were still crossing the runway. The Aircraft Y made no calls for entering or taking off from the runway; and climbed over us as we were finishing clearing the runway. I would estimate we had 200 feet of vertical clearance as they passed behind us. The Aircraft Y proceeded to depart the pattern without radio calls. When the student and I were clear; we used the replay feature on the G100; and could not hear any calls made from the Aircraft Y for takeoff or holding short. I've learned that even if the runway looks clear; and if there are no calls indicating someone has intentions to use it; we should still be extremely vigilant for scenarios like this. We can't always anticipate what others will do.