Battery kill switch.

I have a 1-wire alternator with the charge wire/cable going to the same side of the kill switch as the battery. The cable on the other side of the kill switch goes back up front, but to the starter, then relay.

The wire/cable between the alternator and battery will stay hot with the switch off. But that set-up does kill the starter/relay cable.

You probably still have voltage going from the alternator to the starter and/or relay and the output keeps the engine running without the battery.