[jbonidy]

My lawnmower will not stop running once it starts. I tightened the cable that runs from the handle to the engine, no luck. I saw a green wire that is loose - looks like it should be plugged into something. Could this be the problem - is this a ground wire? Do lawnmowers have ground wires?

[KISS]

Lawnmowers typically have a kill wire. When the kill wire is grounded the engine stops.

Look at the throttle linkage toward the SLOW side. The linkage usually makes contact with a metal clip. This is where the wire goes.

[MOWERMAN2468]

Yes, that could be the "ground" or Kill wire. Look at the throttle linkage close to the carb and see if there is a plastic block that has a small thin piece of metal that is straight and a piece shaped like a hump, then depress the straight piece, and insert the end of the wire, be sure the wire is stripped at the end.
In a pince and during troubleshooting, I have placed a plastic zip tie tightly around the boot of the spark plug wire to pull the long tail end of the tie in case I couldn't kill the engine. The zip tie works great and doesn't shock you.