A PA28 instructor pilot and his student experienced engine failure due to a defective fuel selector valve that failed to stop movement beyond the detent; shutting off the fuel supply.

Narrative

During a student pilot training flight on Jan/XA/09 at around XA40 pilot monitoring; my student and I experienced an engine failure due to fuel starvation. We were conducting a training flight in the ZZZ airport traffic pattern for Runway XX. After 4 landings/takeoffs; my student switched from the right fuel tank to the left fuel tank. The fuel selector detent/lock did not restrict the selector from turning to the 'off' position as designed. Although I normally confirm the fuel selector is in the correct position visually during the change of tanks; I did not this time. During our 5th takeoff and climb; our engine suddenly failed momentarily; and ran very rough following. The engine failure occurred at roughly 500-600 FT AGL. This failure due to fuel starvation was the result of the fuel selector switch being placed about 1 inch to the left of the left tank which is toward the 'off' position. Normally; the detent/lock prevents this situation; however; the lock malfunctioned and allowed the fuel selector switch to move toward the 'off' position unrestricted. This was confirmed by the ZZZ Maintenance Department and I was told to squawk the item for repair. I declared an emergency immediately to ZZZ Tower and landed opposite direction of current traffic on Runway X uneventfully. Clearance and priority were given by ZZZ Tower to land on any runway appropriate. Due to there being an uneven/mountainous terrain to the east of the airport and only partial power loss of the engine; I decided this was the best course of action. In the future; I will check and double-check the position of the fuel selector and have my students announce any movement of it verbally to avoid this from happening again.