I don't believe the fuel solenoid would be relied upon to shut off the engine. I'm having fuel solenoid problems too. I tested my plunger and it did not retract, so I cut off the plunger/stopper.
I think the symptoms of a bad fuel solenoid vary from engine to engine. In my case, if the engine had been sitting a few minutes, my engine would start, but then immediately die. I believe this is because, given time, enough fuel leaks by the fuel solenoid to start the engine, but then it shuts down because it can't get fuel flow to keep running.
I tried to simply cut off the plunger under the assumption that the engine would then run fine with the only side effect being the back fire when shutting down. So after doing so, the engine will now start and run, but it runs extremely rough. I think it's running rich but there's no carb adjustment to play with, so I'm not sure. I guess I'm going to have to pony up the $50 for a new solenoid, after all.
In summary, with the plunger/stopper removed from the solenoid, my engine will start, but doesn't run smoothly. It shuts down immediately when I turn the key off. It actually does not backfire when it shuts down (so maybe it's running lean instead of rich).
Before realizing the problem was the fuel solenoid, I took the carb apart and soaked it in cleaner. While I thought that I did a good job putting it back together, maybe I damaged it or put it together wrong because the motor ran great prior to incurring the fuel solenoid problem.
Has anyone else had experience disabling the fuel solenoid the way I did? Could the plunger being cut off of the fuel solenoid cause the engine to now run rough, or do you think I have something wrong with my carb, now?