Homeless families already in emergency shelters, including migrants from other countries, may be eligible for a state-run program that provides up to $30,000 over two years to find stable housing. The program, HomeBASE, has long served homeless families with children or pregnant women living in the emergency shelter system, which provides temporary housing under state’s decades-old right-to-shelter law. About half of the shelter system houses Massachusetts residents, according to state officials. Resettlement agencies are also working with Gov. Maura Healey’s administration to stand up a pilot program that would, according to one draft plan, help up to 400 migrants in...