Being you only mention 'the coil' and not coils, I assume you have the opposed twin engine which only uses one ignition coil.
If you have ANY voltage on the wire to your ignition coil (its actually an ignition module-it contains the ignition trigger circuit too.) that is the problem. And feeding 12v. to an ignition module is a quick way to ruin the trigger. That little wire is to ground the spark when you want to stop. It should be connected back through the wiring harness to the ignition switch where, when the switch is in the off position, it is connected to ground.
Is there any chance you changed the ignition switch recently? I've ran into several instances where my customer went to the box store and got a switch that looked 'right'-it had the same number of tabs on the back, but those pins didn't work the same circuits as the original switch.
The stator that charges the battery has nothing to do with ignition on those engines.