I suspect it would try to tear itself apart. On a normal elevator when it is deflected downward, the air loads try to push it back up, ie., it tries to return to neutral. Another term for this tendency is that the surface is stable. Now imagine an elevator on the leading edge. When it deflects down the air load will try to push it further down. If the air load is great enough,and the control linkage weak enough, the elevator will flip clear over backwards. Note that an all flying stab, the stabilator, has more area behind the pivot point to provide the stability. I used to own a full size Cessna 170. It had a warning placard that prohibited "whip stalls." These are close to tail slides. Cessna didn't want pilots to rip that great big rudder off by "flying" backwards.