You get several warnings at various percentages. I think the last is at 2%. The iPad shut down a few minutes later.
It should not hurt the battery. The iPad shuts down before the battery can be harmed. However, never leave a fully discharged iPad unplugged for an extended period. If you fully discharge it, then place it on a charger as soon as possible. It is possible that slow battery leakage will eventually fully discharge the battery, reverse the current in some of the cells, and cause damage. By soon, I mean within a day, not x number of seconds.
Hold in mind that the 1-100% charge displayed for a battery is the usable range, as determined by the devices software. The physical limits of the battery are hidden from the user. Pretty much all modern electronics devices will prevent you from over or under charging and hurting the batteries.