Ok, so a bud of mine has a set of these he is selling. He tells me that when the car is running, they work fine. However, when the car is off, sometimes it doesn't turn the lights on.

Is this normal? Do they draw that much more current from the battery that this is a safety feature?

 

First of all I have no experience with aftermarket HID systems; however, on factory systems, the computer will switch the HIDs off and turn on the high-beams during certain conditions. These conditions are usually below 9 volts, and is used to save the bulbs.
HID bulbs require high-voltage to turn on. For factory lights, there are three stages:
First stage (startup stage) will supply voltage pulses anywhere from 600 volts (newer systems) to 24000 volts (old systems), these pulses are used to start the gas in the bulb to turn on, once the bulb is started, the system goes into the second stage.
The second stage is started once the arc inside the bulb is established, it basically warms up the bulb and the length of time is determined by the temperature of the bulb during startup and during warm-up. The second stage can last up to approx. one minute, and is used to supply a greater voltage than stage three to warm up the bulbs. Once the bulb is warmed up sufficiently, the system goes into a stage three.
Stage three is known as the steady state; once the bulb hits a 35 watt power level, the voltage levels off to approx. 55 volts; depending on vehicle.
These bulbs are very expensive to replace, so I can see why there would be a cutoff if the vehicle can no longer supply the high-voltage required.
However, I cannot say for sure this is true for non-GM HID systems. I would contact Phillips and ask them if it is normal.