* Her father, Sanzenin Souichiro, was a notorious gambler. He spent a significant portion of the Sanzenin family fortune on gambling, leaving Nagi with practically nothing after his death.
* He made a series of terrible financial decisions. These included investing in a company that went bankrupt, and losing a large sum of money through a fraudulent real estate deal.
* His death caused a major financial setback for the family. The Sanzenin corporation was left in dire straits and the debts were quickly mounting, leading to a complete loss of their assets.
* There was a legal battle surrounding the inheritance. Nagi's uncle, Sanzenin Kenzo, tried to claim control of the inheritance for himself, arguing that Nagi was too young and irresponsible to manage it. However, this attempt failed, and Nagi was officially declared the sole heir, though she ended up with nothing.
In short, Nagi lost her inheritance due to a combination of her father's poor financial management and the unfortunate circumstances that followed his death. This event sets the stage for the series, as Nagi is now left penniless and has to rely on Hayate to support her.