n.b. most laptop / phone / tablet batteries have fairly sophisticated controllers built into them and the % charge you see on the device may not be the exact % charge in the cells. So running your laptop to 0% may still not be the full discharge (presumably to prevent this exact problem).

That said, I did own a Sony laptop that had a battery saver option where it would limit the charge to 80% in order to prolong battery life. I can't remember if this actually meant "displayed charge = real charge - 20" or was capping the charge to 80%