I’m not a hardware engineer, I write software and find security holes for a living.
That said, I know that Lithium-Ion batteries like to have their charge between 20 - 80% of their overall capacity to extend their lifetime. I also know that discharging a battery down to 0% is not advised. Will it cause damage? No idea. Will any protective circuitry be able to “run” if the battery is at 0%? Probably not. I think that the protective circuitry is in place to stop the battery from charging too much, but I’m not sure about anything to prevent damage if the battery goes down to 0%. Discharging all the way down to 0% too often would probably have some type of lasting effect, I just don’t know what.