Does it make sense though? Either:
- the family is plagued with crazy bad luck that was only countered by Sachi's maxed out luck stat, or
- there's a karma force in effect that cursed the family for throwing away luck like that (perhaps a luck vacuum happens whenever she leaves a place?), or
- by complete sheer coincidence the crazy bad luck happened right after she was kicked out and without her presence they just happened to be defenseless against that bad luck.
While it's all possible, we haven't seen anything that would suggest either the first or second possibilities and the third one would mean that her having been kicked out didn't directly cause the family's sudden misfortune. Heck, the first one shouldn't even be possible if the family was thriving before she was born.
I'm not kicking the story for it, but I will say there's enough room for more clarification imo.