Bill Oliver is one of Biff Loman's former employers. He is introduced to the plot when Biff and his brother, Happy, tell their father that they're considering going into the sporting goods business. Willy is excited about this plan, and believes that it presents an opportunity for success. (During the play, Willy, of course, becomes excited about a string of plans that seem to present opportunities for success, all of which ultimately fail.) Willy tells Biff that he should ask Bill Oliver to invest in his business idea.
Reluctantly taking his father's advice, Biff meets with Bill Oliver. He waits for six hours to see Bill, and when Bill arrives, he doesn't even recognize Biff (and he certainly doesn't invest in Biff's business idea). When Biff returns home, he plans to tell his father that the plan has failed. Instead, before Biff can tell him, Willy reveals to his family that he's been fired. Biff can't bring himself to add to his father's misery by telling him the truth about the meeting. So, instead, Biff lies to his father. He tells Willy that Bill Oliver is considering making an investment and is talking it over with his partner.
People often talk about Death of a Salesman as a play that reveals the American dream to be a dangerous myth. In this reading, Willy Loman is the victim of a false promise: the promise of success in a country rich with opportunities.
But, as the subplot with Bill Oliver suggests, family members play an important part in preserving the myth of the American dream. The play shows how family members hide from each other the fact that failure in America is not only possible, but common. Sometimes the family members do this out of selfishness or pride, and sometimes they do this out of love or worry. The subplot involving Bill Oliver raises important questions about the ethics of telling the truth, when it is kind, and when it is not, and shows how family relationships are one mechanism by which the American dream is perpetuated.