The car would not have lowered if the case was that it slipped traction in the up direction. If it was overspeeding in the up direction most likley it would have tripped the overspeed switch on the governor, top final, both of which is in the safety circuit. 21 is not a highrise.
Ok...If I still remember the jist of this story correctly, there was no slipping traction, or overspeed involved in that particular case...
The whole plot revolved around the fact that the numbers on the floor counting-off display have somehow reset themselves, while the elevator was traveling in the upwards direction and started counting back from the ground floor, when in fact it was already passing a much higher floor...
In this story/legend, the elevator was simply confused at which floor it really was, so if it were a 21 storey building and the counter has reset back to 0 around 15-th floor this would mean that there were only 6 more floors available, while the elevator would somehow "think", that it still has the full 21 floors to go...