Every player at any moment has a residency in one region: it allows you to take part in elections, work (if your region has a restriction) and travel without restrictions. Residency in any region of the state allows you to do all that is allowed in state.
Player can not lose his residency, he can only change it from one region to another. In case if residency is issued by leader (this is regulated by a specific law) you will have to send a request for your residency and wait for state leader to approve it. You can send request on region page.
Leader will decide if you can take residency in this region.
All new players start with a residency in the region which is closest to their real life region or Sao Tome Principe region(if game cannot detect your real life location).
Besides residency you can ask for a work permit. This will allow you to work in the region/state and you won't have to change your residency. You can have 3 work permits max, if you already have 3 permits then your newly issued 4th permit will replace your oldest work permit.