People are idiots and some of the bigger idiots see it as an act freedom to totally dissable all safety switches.
The small wire on the coil is a kill wire and should be open circuit in the run position & ground in the off position.
On a lot of mowers the ground is provided through the key switch by a short ground strap going to the G terminal on the back of the switch
And some others use the body of the switch to create the ground path
If you have to use it before you have time to find the fault & repair it then run a wire from the magneto to the drivers area where you can grab it and make a ground contact to stop the engine.
There is a brake somewhere on the mower
We don't get Castle Garden ( or any other Stiga products apart from STIGA ) so I have no access to your owners manual
If there is a clutch pedal, it doubles as the brake pedal