The falling action of a story occurs just after the climax. The climax in this story is when the main character, Anne Shirley, wins a prestigious scholarship to university. She has worked hard and earned a fine reward. This is the pinnacle of her success, after her inauspicious beginnings as an impoverished orphan, taken in - at first unwillingly - by middle-age spinster Marilla (although Marilla's brother Matthew takes to Anne from the first). However, the falling action brings about an unexpected obstacle to what appeared to be a fairy tale ending to the story. The falling action sees the sudden death of her foster parent Matthew from a heart attack, and the loss of his and Marilla's savings when their bank goes bust.
These combined traumatic events make Anne feel that she can no longer leave Marilla alone to go off to university in the city. This means she has to give up her big chance to get out in the wider world. However, she is more than happy to do this, and stay on at Green Gables to take on a modest teaching job in the local rural school, as she loves Marilla and Green Gables above all else. When Anne makes her decision to stay with Marilla, this leads to the resolution. At first she feels great sorrow, but on making her decision to give up the scholarship she gains 'a smile on her lips and peace in her heart' (chapter 38). In short, although she has had to forego material and social success, she has achieved a moral and spiritual victory.
The story is thus brought to a successful conclusion. Although there is still sadness at Matthew's death, Anne finds fulfillment in supporting Marilla; it is her chance to repay all that Marilla has done for her. Marilla is deeply grateful for Anne's support. Furthermore, Anne finds a new friendship with her old school rival Gilbert Blythe, and there are hints of a burgeoning romance between them as well.