Karen and Jack meet at the hotel bar in Detroit. Karen starts off by playing a make-believe game that they're other people and not a cop and robber chasing each other. Jack plays along for a moment and then ignores it, taking a more adult view about the relationship the two of them are building. Karen quickly realizes that he's right. Meanwhile, the movie is flash-forwarding to the obvious point of where this is all leading: back to Karen's hotel room for a round of awesome sex.
After the round of awesome sex, Karen tries to rationalize it and deal with some guilt issues, calling herself stupid for sleeping with a crook. Jack angrily calls her on it, that while bank robbers - himself included - are stupid, she isn't. She rejoins him in bed.
And when Jack leaves, he leaves behind the gun she got as a gift from her dad, the "excuse" she had for chasing him. While it's the same gun she'll shoot him with at the end, it's a sweet gesture.
Karen with her dad. Early on they act as though their relationship is strained, but during the rest of the movie Karen trusts him enough to talk about her conflicted feelings about Jack, while her dad - overprotective as he is - clearly wants what's best of her, even if that means her hooking up with a bank robber.