It's the more rural areas that are putting requirements on people coming into their states, not cities/states keeping people from leaving. (And the requirements I'm aware of may weekend getaways harder but they're not a real barrier for someone making a long-term move.)
I also remember seeing in news some states mandating quarantine for people moving b/w states. I wonder if that is intended to deter people from making such move out of cities which can lead to the collapse of the cities businesses.