I'm pretty sure her mom died which is why she had to move in with Taihei. Her dad is a rich businessman and yet Taihei has to work his ass off and live in a tiny appartment. He also never showed up during Christmas, Halloween, or Umaru's birthday episodes. He either disowned his children or he did something so horrible, Taihei had to move out and live for himself.
Regardless, I get the feeling that the Nug had a dark past. I hope it becomes clear at some point in the manga.