Well, I'm thinking she's the reason he went "full ham" on those assholes attracting the attention of the police and getting himself sent to the island in the first place. He seems to have decent self-control so whatever sparked that outburst can't have been good. He feels like he's let Liv down, and we know that Liv is/was protective of Teagan. He's not happy about being on the island, but he accepts his fate which suggests that whatever Teagan's situation, he seems to feel like he can't do much about it. (If he thought she needed saving, I think he would be much less willing to wait out his time calmly.)
I've become kind of jaded and pessimistic in my old age, but all of this doesn't seem to be suggestive of a "good end" for Teagan. Hope I'm wrong 'cause she's a cutie!