The purpose of an anti-backfire solenoid is to prevent the engine from backfiring when the ignition key is turned off. When the ignition key is turned off, the solenoid stops the flow of fuel to the carburetor, which prevents the engine from continuing to run. However, if the solenoid is defective, it will not be able to stop the flow of fuel, and the engine will continue to run. This could cause a backfire, which could damage the engine.
However, a defective anti-backfire solenoid would not prevent the engine from turning over. The starter motor is not connected to the anti-backfire solenoid, so a defective solenoid would not be able to stop the starter motor from engaging the flywheel.