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.
That's what I was getting at. If we allow the "State" to reguate all activity not denied to it by the Constitution, then "those in charge" will find some way to stop their laws from changing. We both know that the "people" retained the rights, and gave certain powers to the "State" via the state constitution. But I interject that takes a direct democracy and allows for the "State" to usurp rights based upon a majority or super-majority of votes. Either we, as humans, have certian righths that can not be taken or "given" to a group, or we are governed by the whim of man. We can not have both, really.