Under the scenario that "States" can regulate all activity not forbidden to it by the Constitution, I would assume the people living in such a state could come up with a law to prevent this from happening.
They couldn't prevent people from moving into their state. That would like be ruled as interference with interstate commerce.
More likely the state would attempt to prevent newcomers from voting. Possibly by delaying new state residents from voting until they have many years of residency. Or states could make constitutional changes that would require super-majorities to change laws already on the books.