We understand here that what the speaker cannot stop are her purposeful activities. A purposeful life has goals, and one searches for means toward those goals. We conceive metaphorically of purposes as destinations and of the means to those destinations as paths. When we think of life as purposeful, we think of it as having destinations and paths toward those destinations, which makes life a journey. Thus we will speak, for example, of destinations being mapped onto purposes.
Life is a journey with a stopping point, and that stopping point is death's departure point.
Consequently, death too can involve a journey with a destination. So we speak of going to the great beyond, a better place, our final resting place, the last roundup. In Greek mythology, when you die, the ferryman Charon carries you from the shore of the river Styx across to the underworld. In Christian mythology, you ascend to the pearly gates or descend to the gates of hell. Other religious traditions, such as ancient Egyptian, also conceive of death as a departure on a journey.