A fake degree? Its been done. Sometimes they're caught, sometimes not. Sometimes the employer doesn't care, as long as they have something in their hands that looks official. Some employers will even help with the fabrication process.
The problem is that it just potentiates the problems around dishonesty in business in many parts of east Asia. The idea of 'if you can't beat 'em, join 'em' just isn't sensible in this circumstance. If he ends up with problems with the police/government, his own Embassy/Consulate won't help him much. Lawyers attached to the Emb/Cons won't even be interested, as its a losing situation. Honesty really is the best policy.
Is a degree really all that difficult to get? If your friend is looking to start a career in teaching, he'll eventually need a degree, so why not get it now? If he's looking for an adventure, there's better ways of doing that than ESL in Korea.