In a broad sense of the word, betrayal could apply to the cause of each of these protagonists' suicide. In other words, each character is betrayed by the society in which he/she lives. Willy Loman, for instance, put all his faith in his version of the American Dream: working hard and being well liked would result in financial success. As he tells Howard:
And old Dave, he;d go up to his room, y-understand put on his green velvet slippers---I'll never forget---and pick uphis phone and call the buyers, and without ever leaving his room, at the age of eighty-four, he made his living. and when I saw that, I realized that selling was the greatest career a man could want.
His career as a salesman which he thought would be lucrative and rewarding has resulted in frustration, alienation from his son Biff, and being cast out from his job like an orange peel. Willy's malfunctioning appliances and the apartment housing encroaching up his own yard are symbols of Willy's failures and disappointments as a saleman. Working for a firm for thirty-four years has not resulted in the success he had hoped.
Hedda Gabler also is betrayed by her society. She is a strong, attractive, ambitious, and intelligent woman frustrated by her role as a woman in her society. She dreams of having a great influence over others; she dreams of having true power, perhaps in the form of a political career. But she is trapped by her role as a wife to Tesman and the expectation of a baby, the roles of wife and mother, which seem to be her only options if she desires any kind of social status. She does want to be a help-mate to a man as Mrs. Elvsted is to Lovborg, nor an invalid caretaker, like Tesman's aunt Bertha.
As a result, her desire for power turns into a negative force when she destroys Lovborg's manuscript and encourages him to commit suicide: "the last great act, with its beauty!" Ultimately, though, Hedda has no real power, no true influence over another. Men control her. All she can do is take her own life.