If its not in the shut down checklist it won't get changed and it maybe impossible to change depending what bus the transponder is wired into post engine shut down.
I can and do leave the aircraft how I have just flown it. If the pilot coming to the aircraft isn't capable of checking that everything is order like I do when I take an aircraft over they are not fit to be PIC.
When you set your squawk you check the ID if you can't remember to do that add it to your checklist.