Response of the stabilizer to a failure of the jack screw or its nut and braking system would be greatly influenced by the position of the attached elevators. The horizontal tail normally carries as downward load (less so at aft CG, more so at forward CG). With the stabilizer hinge line forward of its center of pressure, the load on the jack screw is usually in the direction associated with rotating the stabilizer in the leading edge up (i.e., airplane nose down) direction. If the linkage controlling stabilizer position were to let loose I would expect the stabilizer to rotate in that direction causing the airplane to pitch nose down. In response (either by way of the autopilot or the crew) the elevator would be commanded in the airplane nose up direction (elevator surface trailing edge up) that would put further moment on the stabilizer to drive it in the airplane nose down direction.
We also need to remember that the lift generated by the tail is only a small portion of the total lift of the airplane. For the overall airplane to enter an essentially ballistic free-fall the wing angle of attack would have to decrease to that for zero lift. A horizontal tail mechanism failure that allows the stabilizer to float will result in nose down pitching moment that would tend to decrease wing AOA, but it is not correct to assume that a floating stabilizer leads to the wing experiencing AOA corresponding to zero lift. It is very possible that such a failure would result in sufficient nose down pitching moment to drive the wing to a significantly negative AOA to cause negative g.