So, from what I can gather she really was an "escort girl" in a seedy part of town and the salaryman helped her out of that lifestyle to which she then became a police officer who patrols that seedy part of town.

They were talking to one another, but the joke is that both her old life and new life have parallels so it was actually the viewer who misinterpreted what she was saying; though it was done on a meta level.

That's actually really clever. A little confusing, sure, but clever nonetheless.