Despite being the third clone of the Jane series, 3Jane is her own woman. She loves to party and have fun, but her definition of fun extends a wee bit beyond water slides and ping-pong if you know what we mean. She enjoys inviting odd, eccentric, and, in most cases, twisted people into her house for kicks. People like Riviera. This habit may seem like a bad one, but she's protected by a ninja assassin, so it's all in good fun. Plus she has obscene amounts of cash available to her, so she can pretty much do what she pleases and get away with it. You know how it goes.
Ah, but one thing she can't get away from is the fact that she's a Tessier-Ashpool. In her essay on Straylight, she mentions that the TA family "sealed [themselves] away behind [their] money, growing inward, generating a seamless universe of self" (14.108). Yep, that does not sound like a family we want anything to do with. And of course 3Jane's actions seem to be an attempt to thwart her family's inward spiral, from inviting thieving and imbalanced houseguests to manipulating her father's cryotube to induce madness (19.37). Blame it all on the genes. Yet, it's debatable as to whether she is succeeding or not given how the family self-destructs around her.
This leads to the question of why 3Jane gave Case the password to the Straylight's database core. Was she trying to break her own personal downward spiral? Was she trying to fulfill her mother's wish and therefore extend the family's legacy? Was she trying to free the Tessier-Ashpools from their self-made burden?
Once again we're left with tons of questions and absolutely no answers. Suffice it to say that 3Jane's an example of what happens when you've got a ton of moolah and not much of a conscience in the world of Neuromancer.