San Fermin was decapitated, though it is sometimes claimed that he was tied to a bull and dragged through the streets. While convenient for the legend of the San Fermin festival, it was actually Saint Saturninus, the bishop who baptised San Fermin, who was killed in this way.
So what is the connection between San Fermin and being chased through the streets of Pamplona. Mere coincidence of timing. Read more about the Origins of the Pamplona Running of the Bulls.