Mrs. Stevenson is an "invalid" who is bed-ridden due to an unspecified illness or condition. For the duration of the radio play, Mrs. Stevenson repeatedly (and unsuccessfully) tries to reach her husband on the phone because she is worried about her safety. Mrs. Stevenson is typically attended by a nurse, but we learn, through the protagonist's conversations with the telephone operator, that she has given her nurse the night off.
Throughout the course of the radio play, Mrs. Stevenson grows more and more agitated, demanding, and panicked. She is afraid to be home alone, since the patrol officer on her block has left, and her calls to the police (they don't seem to be worried for her safety) and then to a hospital (she wants to hire a nurse for the night) are unsuccessful.
We learn, at the end of the play, that Mrs. Stevenson's fears were justified. However, many audiences don't feel much sympathy for her because of her behavior. (Many readers/audiences describe her as rude and/or annoying.) Ultimately, much of the way audiences feel about Mrs. Stevenson depends on the actress who plays her.