Cinder's escape from prison occurs at the very end of the book. This ends the book on quite a cliffhanger, because readers want to know how she continues the fight against Levana now that Cinder is free from prison.
Start looking in chapter 37. The chapter begins with Cinder feeling like she has to accept her fate and stop worrying about past actions. As she is doing this, she hears a commotion. It turns out to be Dr. Erland. A guard tries to tell Erland to leave, but Erland uses his lunar powers to brainwash the guard.
Erland comes bearing gifts. He has a bag that contains a new cybernetic hand and foot for Cinder. They are perfectly fitted for her and come with a variety of very useful hidden gadgets. Cinder doesn't see the point, because she still believes that she will be dead in a few days. Dr. Erland says that can't happen, and he tells Cinder that she must escape prison and join him in Africa, where there is a community of lunar fugitives. Cinder still doesn't see the point, and that is when Erland tells Cinder that she is Princess Selene.
Chapter 38 begins with Cinder reeling from this new information. Erland urges her to escape using her lunar powers, along with the new hand and foot. The book ends with Cinder deciding to do this, but it ends just as Cinder cuts out her ID chip and begins her attempt.