You must have a really shit car. Mine has an electronic oil guage, and warns me if there's is insufficient oil in the spare area - the sump. If I wish, I can press a button and get it to show me exactly how full it is.
Even on shit cars, the light means it's not pumping well. If you stop as soon as that happens and add oil, you cannot possibly damage the engine. Do you seriously think they'd fit a warning light that tells you you're too late?
What about your fuel warning light? Does that come on when the tank is empty? Telling you what you now already know as your engine has stopped? Or perhaps it tells you when you have 40 miles left to go, so you can fill up. Use some f****ng common sense.