Backfire-after turning key off

Not if the fault is no power on the start side. :D
The ignition switch can be bad on the start side and fire a spark only when you let go of the key, but most engines I have had fire up at that point anyway just because they are already spinning.
They don't usually backfire though as I would call a backfire.
There would have to be two faults, IGN1, and IGN2. But, it backfired, that happens if it has even cranked with fuel present, coil energized, then key off. If the ECM is not triggered, shorted, or coil- grounded, key off makes a spark. With V8, high probability it will pop on some cylinder, but not in correct time.