What did Willy's family gain by his death?
Arthur Miller's famous play Death of a Salesman deals with the fall of Willy Loman, a traveling salesman, who lives in Boston, Massachusetts, with his wife Linda. He also has two grown sons, Happy and Biff. We are told early on in the play that Willy has been trying to kill himself. In the play's final act, Willy does manage to kill himself, supposedly so the insurance money could be used to help Biff achieve some successful business venture.
What the Loman family gains from Willy's death may be a matter of speculation and personal interpretation. If the insurance claim was upheld, then they could have profitted financially from his death. However, if his death was ruled a suicide, then presumably his life insurance policy would not pay out.
Each of the surviving members of the family will gain something different. Willy's wife Linda will acquire some measure of financial freedom and perhaps freedom from mental anguish over her husband and their financial future since they had apparently just paid off their house before Willy died. Linda speaks the play's final words: "We're free and clear. We're free."
Happy, it appears, will inherit his father's dream of becoming an important businessman in the city. He declares to Biff that
"I'm gonna show you and everybody else that Willy Loman did not die in vain. He had a good dream. It's the only dream you can have -- to come out a number-one man."
Thus, it appears that Happy gains some purpose for his life, even if that purpose is following in his father's footsteps. It is difficult to image that Happy will live up to his own name.
As for Biff, he also gains some sort of clarity for his own life. Biff concludes that his father's dream was the wrong sort of dream and that Willy "never knew who he was." After Willy's death, though, Biff now declares, "I know who I am, kid."