It's probably a problem with throttle cable adjustment. If the cable has rusted so it won't move properly, it needs to be replaced. Otherwise, over time, reefing on it may have pulled the lower end through the bracket so it isn't pulling all the way past Idle to the Stop position. There also should be a Magneto/Electronic Ignition Kill Switch that cuts the ignition when the throttle is put all the way to the stop position.
If this is the Honda GVX160 engine, here's a representative of instructions on how to properly adjust the cable and possible location of the kill switch (yours may vary by serial number range or if it's the Kohler engine, a whole different mechanism). If the cable is misadjusted, the kill switch doesn't operate, also if dirt got in there or the wire fell off, the switch won't operate.
(The engine manuals are readily available online, look up by Engine Make, Model and Serial Number,)
Ignition circuit on the Honda GVX160 shows that there is a kill switch.