A light aircraft instructor pilot reported the student descended below their intended altitude and flew below the required altitude over a populated area and terrain requirements due to a nearby obstacle.

Narrative

While conducting an End-of-Course (EOC) flight with a Private Pilot student; we were operating in the vicinity of ZZZ with the intent to descend and set up for landing. The student was the pilot flying; and I was acting as the instructor and safety pilot.During the descent phase; while operating over a congested area; the student initiated and continued a descent beyond the intended altitude. Due to task saturation associated with airport identification; descent planning; and landing preparation; the student did not arrest the descent as expected. As a result; the aircraft descended to approximately 5;600 - 5;700 feet MSL.I recognized the altitude deviation as we passed in proximity to a charted obstacle with a listed elevation of 5;200 feet MSL. Upon recognition; I immediately took control of the aircraft; applied full power; and corrected the flight path to regain a safe altitude. The aircraft maintained obstacle clearance; and no terrain impact or loss of control occurred. No other aircraft were observed in conflict; and ATC was not involved.Contributing factors included high student workload during a critical phase of flight; fixation on landing setup; and delayed instructor intervention. As the instructor; I acknowledge that earlier monitoring and more assertive altitude callouts could have prevented the deviation from minimum safe altitude expectations over a congested area.This event reinforced the importance of heightened instructor vigilance during student evaluation flights; particularly during descents over populated areas. Corrective actions include establishing more explicit altitude constraints during EOC flights; earlier verbal callouts; and proactive instructor intervention during high-workload phases of flight to prevent recurrence.