For more than a decade, Shao Zhao has called Chinatown’s sprawling, green stucco Hillside Villa apartment complex her home. Perched off Cesar Chavez Avenue, the building is just a short jaunt from businesses that cater to neighborhood’s majority-immigrant population, making it the ideal spot for Zhao’s 55-year-old mother, who speaks Cantonese and rarely drives outside the city. For years, the pair never saw a reason to leave. But in spring of last year, they received some startling news: In 12 months, the building’s affordability covenants were set to expire, and their landlord, Thomas Botz, would be raising its rents to market rate.