My understanding of the IAC is that the idle air control valve basically supplies air to the cylinders/engine when the throttle body is completely closed/shut. Per wikipedia, "The ECU can control the amount of air that bypasses the throttle when the throttle is fully closed, thereby controlling the engine's idle RPM."
Well, the engine can't run without air and fuel (and spark). And... if the IAC is bad (Say a bad solenoid, or the valve itself is jammed) -- you have symptom's of really rough idle, but your engine still runs.
How is the engine getting air into it with a bad/faulty/clogged IAC?