Independence of the new country will be for all who lives within. If you are a law abiding citizen who contributes to the economy of the new country there is no reason to ask you to leave.
However, the immigration laws will be tough on everybody. If you are an illegal alien you will deport in line with the new immigration laws. If you commit acts like unlawful protests, stone throwing, disruption of services, etc, you will be subjected to strict laws which may find you being deported.