When a tail loses lift the nose pitches down because the horizontal stabilizer pushes the tail down for stability.
Actually it is not for stability, but for moment compensation. The moment compensated is the nose-down pitching moment produced naturally by any cambered airfoil with attached flow. So when stalled, this pitching moment may disappear, and no more downforce on the tail is required. But that depends heavily on the specific airfoil characteristics, whether the flow separation starts at the trailing edge and extends forward, or whether it starts at the leading edge and reattaches further aft.
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Actually it is for stability....modern jets are still aerodynamically stable.. I have done the hours and hours of heavy calculations. In essence your wasting fuel ( big wing pulls up, tail down ) by this downward forces, but it's the only way to make the AC naturally stable without computer systems as in fighter jets