250 Yamaha 4 stroke not looking good

[steplift20]

250 Yamaha 4 stroke only runs when you give it gas( push the throttle forward) stalls in neutral , won't run
Changed all the filters
Pulled the spark plugs ( this is where it gets ugly) the bottom plug ,the electrode is gone,broken off. Someone told my son that the motor is toast,
Is there anything that I can check? Anything I missed? I know he needs to replace a throttle cable but what happened to the plug? I'm all ears,thanks