I look at negative experiences (not emotions) the same way I look at lifting weights. It is a stimulus that can cause you to grow stronger. Much like you have to lift weights with proper technique to avoid injury, you have to learn to respond to negative events with the proper cognitive strategy to avoid suffering.

I don't think negative emotions are necessary, however. The benefit comes from learning to process negative events constructively, which people (sometimes) learn to do in order to avoid the pain.