When you get off an elevator, if no one else is ringing for it, it might stay at the current floor, return to ground floor, or go to some other place to minimize the probable delay when it’s next called. But it will stop at some floor awaiting a command.
Generally, when an elevator is at rest like this, it will be closed. (If there is a bank of elevators, then on the main floor it might stay open.) I think this is one aspect of the human/machine interface that the designers got right. Imagine that you’re on the fifth floor of some building, you walk over to the elevator, and it’s just standing there open. Might that seem creepy? Would you wonder if it was working?