That's actually an action. The subject of 抜けちまう is the speaker.
ぬける【抜ける】
4 〔通り抜ける〕
打球は一塁手の足元を抜けた
The (batted) ball got past the first baseman.
トンネルを抜けると目の前に富士山が見えた
When we emerged from the tunnel, we saw Mt. Fuji right in front of us.
台風は日本海に抜けた
The typhoon blew out into the Japan Sea.