When does Miss Maudie show empathy in the novel To Kill a Mockingbird?

Miss Maudie exhibits empathy for Boo Radley in Chapter 5; she also exhibits this feeling for both Aunt Alexandra and Atticus in Chapter 24. 

Although the "foot-washing Baptists" rebuke Miss Maudie for her sins, she is truly a very charitable and warm-hearted woman who is much like a grandmother to Jem and Scout. Certainly, the children feel comfortable asking her just about anything because she replies honestly and with consideration for them. 
In Chapter 5 Scout inquires about Boo Radley and is first told that the man's name is Arthur. To her question about the possibility of Arthur's death, Miss Maudie replies that he is yet alive. She adds,

"Arthur Radley just stays in the house, that's all....Wouldn't you stay in the house if you didn't want to come out?"

She explains further that Mr. Radley is a hard man and that Arthur lives in "a sad house." She recalls that as a boy Arthur would always speak to her: "Spoke as nicely as he knew how." When Scout asks if Arthur may be crazy, Miss Maudie replies with genuine feeling and empathy for Arthur:

"If he's not, he should be by now....What happens in houses behind closed doors, what secrets--"

• Chapter 24

At the Missionary Tea, Mrs. Merriweather reveals her sanctimonious hypocrisy as she speaks of the great missionary work that Reverend J. Grimes Everett performs in Africa while she none-too-subtly reproves Atticus for seriously defending Tom Robinson:

"I tell you there are some good but misguided people in this town. Good, but misguided....some of 'em in this town thought they were doing the right thing a while back, but all they did was stir 'em up."

Because Mrs. Merriweather has made such insulting innuendos against Atticus in his own house and before his sister Alexandra, Miss Maudie fires back at her with a cynical remark, asking if Mr. Merriweather has his food sticking as he tries to swallow it ("His food doesn't stick going down, does it?"), implying that it must be difficult for him to eat food cooked by their black maid.

After this, Aunt Alexandra gives Miss Maudie "a look of pure gratitude" for her empathy. Later in the afternoon, Atticus comes home and announces to Alexandra and Miss Maudie that Tom Robinson has been shot trying to escape at the prison. He soon leaves, and Alexandra is very shaken by this terrible news. She tells Maudie that although she does not approve of all that Atticus has done, he is her brother and she worries about the stress that he is under: "It tears him to pieces....what else do they want from him, Maudie?"
With empathy, Miss Maudie replies, 

"Whether Maycomb knows it or not, we're paying the highest tribute we can pay a man. We trust him to do right." 

Alexandra asks, "Who?" and Miss Maudie replies, 

"The handful of people in this town who say that fair play is not marked White Only; the handful of people who say a fair trial is for everybody, not just us;....The handful of people in this town with background, that's who they are."

Having given Scout's aunt true moral support, Miss Maudie then suggests that they return to the ladies in the other room. Bolstered by Miss Maudie's support and empathy, Aunt Alexandra straightens her dress and re-assumes her role as hostess with renewed confidence.

Miss Maudie's wise and generous heart provides emotional support for members of the Finch family. This warm heart also extends its empathy to them and to others who need it, such as Boo Radley.