It is fitting that Minnie Wright does not appear on stage for a number of reasons. With no physical appearance and no lines, the audiences is unable to form superficial conclusions about Minnie Wright. The audience can not judge her based on appearance and they are unable to judge her based upon attitude or any hasty interpretation of anything Minnie might have said on stage. The audience is in the same position of the other characters. That is, the audience must look at the evidence in order to determine who Minnie and John Wright are/were and what their relationship might have been like.
Minnie's absence can bias an audience. Without an onstage persona, she might be understood in a universal way: as any woman who suffers with a bad or repressive husband. So, this is a bias that can play into an audience's sympathy for her. But her absence is also symbolic of how her husband stripped the life and personality out of her. In this sense, Minnie had been absent for a long time. Mrs. Hale notes how Minnie Wright had been different:
She—come to think of it, she was kind of like a bird herself—real sweet and pretty, but kind of timid and—fluttery. How—she—did—change.
While the men are there in the house looking for evidence to convict Minnie Wright, the women continually find evidence that paints her as a victim. They are able to construct their version of Minnie as "kind of like a bird." The women had also noted that Minnie changed. She used to sing and used to be more full of life. After commenting that Minnie used to sing, Mrs. Hale says that John Wright "killed that too." Mrs. Hale and Mrs. Peters paint this picture of Minnie Wright as one who used to be free like a singing bird, but has now become more like a caged bird. She had become symbolically caged in her unhappy marriage with John and had become literally caged in jail.
With Mrs. Wright never appearing on stage, the construction of her character is completely in the hands of the other characters and, in the end, left to the interpretation of the audience.
So, Minnie's absence gives the characters the artistic license to reconstruct who she was and who she became. The men and women have different agendas and strategies in this construction. Minnie's absence also underscores the idea that her freedom and love of life had been taken from her during the course of her marriage. In this way, her persona and essence had been absent for some time before she took revenge on her husband.