PA-44 flight instructor reported a runway excursion during a simulated engine failure below V1. The event was caused by a less than thorough scenario event briefing and conducted on a narrow runway.

Narrative

Aircraft X was conducting a flight lesson for a multi-engine instructor (MEI) training at ZZZ at approximately XA:45 CDT. Aircraft X lined up on Runway XX at ZZZ. Runway XX at ZZZ has a length of 3;100 ft. and a width of 60 ft. The crew communicated that this takeoff will be simulating an Engine Failure below VR (Takeoff Abort).Flight Instructor (herein after referred to as 'Pilot A') stated that he will be acting as a simulated student; and the trainee student (herein after referred to as 'Pilot B') will be acting as a simulated MEI. The crew acknowledged.During the takeoff roll; Pilot B brought the right engine's mixture to the IDLE/CUT-OFF position. Pilot A maintained both throttles at takeoff position as a simulated student. The aircraft started drifting to the right. In about 1 second; Pilot B brought the right engine's mixture to the UP position in response to the aircraft's drift. Pilot A stated; 'Throttles; throttles'. In 1.8 second; Pilot A brought both throttles down to the IDLE/CUT-OFF position--and applied left rudder. The aircraft's nose was already positioned towards the off-runway direction. The aircraft went off of the Runway XX on the right side and came to a complete stop. The aircraft hit a side runway light with the aircraft's landing light lens installed on the right side of the aircraft nose.After verifying there are no injuries; Pilot A taxied the aircraft to the ramp at ZZZ. After the aircraft was parked; the crew assessed any injuries and/or damages to the aircraft; equipment; and property. The airport manager was notified accordingly.CONTRIBUTING FACTORS-Poor choice of runway with a narrow width for the given emergency scenario.-Poor communication between the flight instructor and student regarding the given scenario.-Flight instructor's assumption that the student would respond correctly due to the previous simulator training.-Flight instructor's attempt to have the student correct it rather than immediately intervening to take over controls for proper recovery procedures.PREVENTIVE ACTION-Choose a wider size of a runway.-Transition the training scenario from an easy to a more challenging scenario.-Be prepared to immediately take over controls when the student does not respond correctly.