Small Engines (Lawn Mowers, etc.): solenoid in carb, hp briggs, ride on mowers

Question
I have a 14 Hp briggs. (model #287707, type#0220.01, code#9308034A) The motor will run by putting gas down the carb.  The solenoid in the carb does not go in once the motor starts to run, so then it dies (it won't get gas).  If you put power to the solenoid it does go in, but I have no power to the solenoid when the motor is running.  Is there something under the flywheel that I should be looking at?  Any help would be appreciated.  Thank you!

Answer
 Hello Justin:

 What is the Application of this Engine? Most of the Engines with the Shutoff Solenoid are Mounted Onto Ride On Mowers and have a Battery to Open the Solenoid. There is a Stator Under the Flywheel that is the Charger for Most Small Engines. The Stator Doesn't Produce Enough Current to Activate the Solenoid until the Engine is Running at Full Throttle. Send me the Make and Model Numbers Off of the Equipment, Please. With these, I can Locate a Breakdown of the Equipment and Better Assist you. Hope this Helps. I am here if you Require More Assistance. Let me know what Happens, Please. Thanks.

 Good Luck

 Respectfully

 John