Let me add that the Armistice in Korea which ended the fighting was signed by the United Nations Command commander.  In the article for UNC, you will note that the ROK relinquished command of its military forces to UNC early in the war.  (This statement is unreferenced.)  Thus, the military of SK (ROKA) was bound by the armistice.  The armistice itself asked or projected that the governments of the parties would begin peace talks in the near future, but this did not occur.  In any event, the fighting was stopped by means of a document (e.g., legal document) that was binding to the parties.  The war had ended.