I think the exaggeration Faye uses [i.e "the men fight over me like dogs"] in this episode really speaks a lot about her insecurities — she felt unwanted by the Bebop, probably due to her issues with trust. Whenever she leaves, taking something (like the money), she's asking them to come find her. She's basically asking them to prove that they want her around.
I'm just gonna say one of the major themes of this show is "Trust", because of the Found Family dynamic and each of the main cast's traumatic pasts (that the show has hinted at by this point).