This is a good question. It is hard to say that Arthur Radley changes in the book, because he does not say much, and he is always in the background. Without direct communication from him, we need to make educated guesses.
If we do this, we can say that Arthur reaches out more to people as the novel progresses. At first, we know him as a recluse who is locked up at home. There is also the feeling that he is not stable mentally and emotionally, as there are many stories about him.
As the novel moves ahead we see him reach out to Jem and Scout. He leaves them gifts, such as soap models, coins, and gum, to name a few. This shows that Arthur is kind and wants to build a friendship. When there is a fire (Ms. Maudie's house), and the kids are outside, he puts a blanket over Scout, which shows more kindness.
Finally, in the climax of the book, when Bob Ewell attacks Jem and Scout, he is there to help. In light of this, we can reasonably say that Arthur changes in the book in that he is more loving and kind in concrete ways. He is breaking out into the world again.