Yes Lead Balloon, as stated, that's the cause.
I think we're getting confused about what we're talking about. I thought you were asking about the electronic ignition and fuel injection system that I was referring to, but you keep commenting on my statements in relation to a standard Lycoming or Continental fuel injection system. This is not a standard system. There is no idle cut off. In the system I'm talking about, each cylinder has its own electronic injector that meters fuel into that cylinder based on crank timing, manifold pressure, rpm, throttle position, engine temperature, fuel pressure, fuel trim setting, and exhaust O2 ratio. As long as the fuel pressure is between 20 and 40 psi, the system meters correctly. Fuel pressure is regulated at 35 psi from before start until shutdown, and the injectors will do their thing as long as there is power to them. Once power is removed, no fuel goes into the engine regardless of fuel pressure.
The point was to provide one example of a Lycoming or Continental engine that shuts down with the key rather than the mixture in response to a question in this thread. Another example is a C85 which does not have an idle cutoff in the carburetor.