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In the play Death of a Salesman, by Arthur Miller, the character of Bill Oliver is an old supervisor for whom Willy Loman's son, Biff, used to work.
As part of the Lomans' tendency to imagine situations that they, later on, believe to be real, Biff lives under the assumption that he is Bill Oliver's best employee and that, in fact, he is a type of partner of Bill Oliver's business.
This is why Biff goes to Bill Oliver to ask him for a loan of $10,000 that would be put towards a down payment for Biff and his brother, Happy, to start a business together. However, during the restaurant scene of the play, we encounter Happy and Biff discussing that Bill Oliver does not even remember Biff when he sees him.
This is the moment when Biff realizes that his life has been a foolish illusion. This is also the moment when he feels it is time to stop the fantasy under which the Lomans continue to live and he decides to confront Willy with the truth about it all.
As the previous answer states, Bill Oliver is a former boss of Biff's. Biff has never been able to settle down long to any job, but he seems to hold out a hope that Bill Oliver might lend him money because he was a favorite employee of his. Happy conceives the idea of a starting a business partnership with his brother, and the money from Bill Oliver would enable them to set up that business.
However, the idea of a loan from Bill Oliver is just another pipe dream of the Lomans', and comes to nothing when Bill Oliver doesn't even remember Biff when he goes to see him. As the previous answer states, this is really the moment when Biff realizes once and for all that his life has just been a "lie"; he was never actually a big salesman for Oliver, as his father Willy likes to pretend, but a lowly shipping clerk:
We've been living in a dream the last fifteen years.
Whatever Willy might say, Biff is painfully aware that his career thus far has been a complete shambles and that he's simply not cut out for the kind of high position in the business world that Willy is always dreaming of. All he has really done is replicate his father's failures. The fiasco with Bill Oliver precipitates the final, fateful showdown between Biff and his father.
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.
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