To an enlightened person there is a permanent state beyond the emotions, which are impermanent. We feel the emotions on one level but on a deeper level, we are observing them. There is a sense of detachment. We recognize that we are not our thoughts and we are not our emotions (which are often generated or triggered by our thoughts). We rest in an eternal peace that lies in the background.
Sometimes people seek enlightenment because they want to be free from all painful emotions once and for all. But we cannot have one thing without its opposite. We cannot have happiness without also knowing what unhappiness is, to contrast it with. Enlightenment is not about cancelling out anything that makes us miserable. It is about being at peace, no matter what thought or feeling comes up.