That is correct, they don't stop the game when 1 side has lost all units, they let the game continue so that the surviving person can continue to collect victory points (usually off his secondary objectives). As Thairne said, you could still have someone who lost every unit win the game if they have more victory points at the end of the game.
Since you both still had units in reserve, you both can bring those onto the board following the normal rules for the game you're playing.
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