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If you look at Act One carefully, it becomes very obvious that Kate is a woman who is unable to move on from the disappearance of her son, Larry. She is presented as a character who is unable to contemplate the possibility of her son's death, and thus she clings on to the vain hope that he is not "missing in action" but will find his way back home eventually and re-enter their lives. Notice how she says to both Joe Keller and Chris that she wants them to "act like he's coming back":
Because if he's not coming back, then I'll kill myself!
Of course, as the play progresses we realise that Kate is so fixated on believing in Larry's safe return because if she accepts he is dead, then she has to accept that her husband was responsible for the deaths of the soldiers because of the faulty parts his factory provided.