When I was a new electrician, one day I discovered I could read 120v across the terminals of an open switch. I was bothered by this thinking someone had wired it wrong, but I couldn't understand why it wasn't blowing up or tripping a breaker when I closed the switch until my boss explained I was reading the voltage through an incandescent light bulb on a switch loop (a cable with black and white wires between a light and switch, with the white being used as a hot, which should be properly marked to indicate its hot status but often is not, and the black being used as the switch leg). When the switch is closed the current passes through the switch, through the load, and returns on the neutral wire to the source.
My question is mainly for trouble shooting odd things out there. So here is my proposed scenario: If someone (an apprentice electrician, let's say) were to open a switch box, or seeing one with its switch missing, mistake the switch loop for a hot and neutral, then pigtail off to add a receptacle, and then if someone else was to return from lunch, not notice the addition and wire the switch back in on the new pigtails, and then, let's say the new receptacle really wasn't used for many years so no one noticed anything amiss, until one day when someone plugged something in...What would happen? What would this look like when the switch is off, when the switch is on? Let's say the item plugged in is another lamp, maybe LED that doesn't use much current. And let's say the original light circuit with the switch is a 100W lamp with system voltage at 122V. I'm curious if the LED would come on only when the light switch is off. I wonder if the LED would behave normally, even being in series with the other light, and what would plugging the LED in do to the original light?