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When panic level reaches the top in XCOM-adherent nations, they choose to leave the program, as it is notified by the Council.
My question is: it is possible to have them re-enter the XCOM program again during the story?
Unless you have mods, which I don't believe you can obtain in the Xbox version, nations that are lost due to terror/panic are lost forever. There is no way to get them back, outside of modding.