Death is a character, a practical concept and a symbolic concept for Troy in the play. Of these roles, the symbolic concept is the most important for understanding Troy's character and his internal struggles.
As a character, death appears to taunt and challenge Troy. The stories that Troy tells about death are fantasies that always emphasize Troy's potency.
In one of the stories he tells, Troy relates how he once wrestled with death and won.
The potency exemplified in these stories is of a type that Troy does not actually possess - the power to change.
Troy lives a life of repetition, though he deeply desires to change the course of history.
His father was brutal and controlling, and although Troy loves Cory, he knows of no other way to bring up a son. Thus, he repeats the mistakes of the previous generation.
Desiring to keep his son from repeating his own course and becoming a garbage collector, Troy ends up managing Cory's life rather ruthlessly and without kindness, leading to a situation of rivalry that ends the relationship. Troy wants to change his son's course in life, in part, because he cannot go back and change his own.
At the heart of Troy's unhappiness is his disappointment at not being able to play professional baseball.
He keeps Cory from playing football because he is overwhelmed by bitterness regarding his own sports career.
If Troy could change anything about his life, clearly his baseball experience is what he would change. Yet, the past is fixed and unchanging like the inevitability of death. This is the symbolic significance of death for Troy and serves as an interpretation of Troy's stories about the character of death.
In his stories, Troy is able to change nature and defeat death. This power remains central to Troy's deepest emotions even as he fails to change himself and fails to avoid the unfortunate repetition of history (by losing his son). Unable to change and accept his limitations, Troy maintains his symbolic "vigilance" against death and strives for superiority over it, failing to achieve either humility or emotional maturity.
In the end, Cory leaves the house for good, and Troy ends the scene with a taunt for death to come.