Well they don't need to be a saint, as none of us are. They just need to learn how to function in society. I think rehabilitation is possible for the majority. Norway seems to show this in that they do not instate capital punishment or life imprisonment, yet have extremely low recidivism rates (especially compared to the US).
If we set the criminally insane aside (a small portion to be sure) the majority remaining need training, motivation, assistance, and separation.
1. Training - many people in prison never learned how to "live productively" if you will - this includes things like job training but also basic life training, etc. Nobody should leave prison with anything less than an high school equivalent education, and training and knowledge on how to cook, clean, etc for themselves.
2. Motivation - the "why bother" needs to be shown and instilled - why bother doing a job when you can just do a crime or drugs instead?
3. Assistance - we shouldn't just dump people out of prison on the street - they don't know where to go or who to contact and it's likely the people they DO know are other criminals, which doesn't help. There should be "outpatient" assistance provided that gets them a job, housing, etc. Call it supervised release as part of the sentence and you could do quite a bit. Provide incentives and security for companies to hire ex-cons, and continue to assist as long as necessary.
4. Separation - it can be vitally important to help ex-cons separate their "con life" from their future life, whatever that may be. Many of the successful ex-cons were in prison for an "accident" (e.g, unintentional murder because they drove drunk, etc) and so their support groups are non-criminals, but the ones who only know other criminals may need to be moved elsewhere for a time.