I'm not sure that it would qualify as a "alternate" ending, but one of the elements I have always found to be unresolved in the novel is the future of Bigger's younger brother, Buddy.
Throughout the novel, we understand the "warning" being issued by Wright: if America does not address its racism, racial strife and violence will continue to grow and potentially destroy very fabric of American life. In fact, unless the issue of racism is dealt with head-on, problems such as those we read about in the novel will only continue to grow "Bigger."
Bigger's fate is sealed; we know his outcome from early in novel. What we do not know, however, is the face of Buddy, the younger brother who idolizes and learns from watching Bigger's interactions with the outside world.
An alternate ending could feature Buddy as the primary character and explore his future and reactions to the fate of Bigger. Does he continue to emulate the attitude and behavior of his older brother? Does he seek revenge on his brother's behalf and thereby produce a "bigger" problem for American society to deal with? Or does Buddy learn from Bigger mistakes and find better methods to address and deal with the racist world he must live in?