I don't think it's a set phrase. I would expect this to be a 'for the purpose of' に like 買い物に行く
As a physical action, 出ていく is subj. exiting the place speaker is at and going somewhere else,
出てくる is exiting somewhere else and coming towards the speaker.
If it's a metaphor and not a physical action, then yes, it's aimed at the speaker.