Atticus' greatest desire for his children is to develop the ability to put themselves in someone else's skin. Lee hits the theme of empathy consistently as the scope of Scout's awareness grows. Lee starts us first by investigating the cruelty of children from several angles, (Walter Cunningham, Miss Caroline's ineptness, etc). The circle widens to further include those who seem to deserve empathy, Dill, Miss Maudie, and those who seem to deserve nothing but scorn and retribution. Mrs. Dubose, Francis and Aunt Alexandra seem to be beyond the scope of empathy. But Atticus is able to guide his children into overcoming the ego-centrism that defines us all in our early development.
Her morphine addiction, withered physical capacity, and marginalized importance carve her into a niche where she is left cornered, frightened and weak. Her only reaction of lashing out violently against a threatening and changing world is understandable, though repulsive.
The children believe that Mrs. Dubose is nothing more than a cranky old lady who lives down the street. When Jem, in his anger at her for insulting Atticus, destroys her flower beds, Atticus insists that Jem pay restitution through reading to the woman. It is through this exercise that the children eventually learn about "real courage" because they do not know about Mrs. Dubose's morphine addiction. The elderly woman has had to take morphine for pain and, unfortunately, she became addicted to it. It was her wish to free herself of the drug before dying, and so when the children came to read to her, she put off taking her medication until they were finished. She sets the timer longer and longer each session so that, as long as Jem is reading, she is distracted from her pain and not on morphine. The children had been previously unaware of her condition, and so they simply thought she was just a mean, old lady instead of a woman in pain. Once the reader is aware of her condition, like the Finch children, our perspective is changed. This helps to create sympathy and understanding for her character's behavior.
Perhaps the purpose of Scout and Jem's adventure with Mrs. Dubose is to juxtapose what the children think is courage (Atticus killing Tim Johnson in one shot) to what Atticus says the true meaning of courage is, "when you know you're licked before you begin..." (Lee 112).
One need only read the description of Mrs. Dubose from chapter 11 to appreciate Lee's style; however, the images of Mrs. Dubose appearing frail and ill with her covers pulled up to her chin are a part of Lee's style that engenders sympathy. Also, Jem's reaction to Mrs. Dubose's death and his and Scout's eventual understanding of her addiction might help us to feel sympathy for Mrs. Dubose.