That is exactly what happens. Here in New Hampshire, we have been inundated by former Massachusetts residents (we call them Mass-holes), who try to escape the high taxes and the excessive regulations of where they came from.
They came here for the ‘Country Life’, and no income taxes. And once they got here, they started pushing for services like Street Lights, Golf Teams at the High School because their kid is a good golfer, and demanding that the town government pick up their trash at the curb-side at their home. Their demands of State and Local government have no limits. And New Hampshire gets closer and closer to becoming another Massachusetts every day.