assuming that the secession movement is peaceful, they can stay or leave as they choose. if it is to the point of secesion, then they would be a small enough minority unable to sway the majority otherwise. no violence. simply an option presented of stay and bear with a new republic, or leave for the known of the old republic.
an option for a peaceful secession does not preclude an amicable break-up. simply a parting of ways for irreconcilable differences
So those loyal to the United States would have to leave. But when countered with why don't you leave if you hate it here so much I hear a lot of posturing and excuses.