In Emily Dickinson's poem "Because I could not stop for Death", immortality plays an important role.
Death is personified in the poem. What this means is that Death is given characteristics, or abilities, which are typically possessed by humans alone. When something is personified, it is non-human or non-living. The object is given characteristics typical to those which only mankind can possess.
That being said, the role of immortality, personified as well, must "go along" for the ride" given women of the time were not allowed to be with a "man" alone if not married to him.
Therefore, the role of immortality is one of a chaperon. There is a deeper meaning to this though. Death must always be partnered with Death given that Death is the one who determines immortality. One can only remain immortal if Death refuses to take them.