That looks like the anti-gonial notch. In general, that happens due to trauma in youth when the jaw is developing, and it can lead to downward growth. I think grafting the notch would probably be the best idea if someone is willing to do that, but that means more cuts, more scar tissue, infection risk, etc.
I'm not sure if that's what is going on, but that's what it looks like, so I'd ask about all that and see what they say.