Happiness, to be experienced, must be sought, pursued and embraced. To be happy, I must want to be happy and take the risk of opening myself to joy. Happiness is not a companion of fear.
So it is similar for suffering. I must have my eyes open, then I can recognize suffering. To accept suffering is to embrace it, envelope it, absorb it in the depths of my senses.
There is no sting. The result is a quiet peace not unlike my experience of happiness.