As recently as 2007, the state placed almost no homeless families in hotels. But the next year, as the economy faltered, the number of homeless began to climb. In Massachusetts, it peaked at 1,793 families living in hotels in July 2011, and the state created HomeBASE, a program to help qualifying families pay rent. The Home Suites in Waltham are home to 90 homeless families with children placed here by the state, both the working poor and the unemployed.