Lets start with an example of the elevator running with the doors open.
First off, there are several circuits that need to be completed before an elevator even attempts to move. Second there is a hardware safety string circuit that must be completed before the elevator takes off. Furthermore, in modern microprocessor-based systems, several inputs points along the safety string, are picked off at several points to do such things as enable the Drive, the usually separate motion control computer, and the usually separate dispatching computer. The back-contacts of these relays are monitored, to in effect, to make sure that these circuits are operational and that the processor can see the the inputs from the back contacts, indicating to the processor that it is unsafe to run the elevator. I know what you're thinking now.