Just to add to this, I’ve found a big factor in the successful reintroduction of an excluded member is the context. If they’re just allowed to return as if nothing happened then they can quickly fall into old habits, assuming that their behavior may now be excused because it’s “understood”. You may also find that their previous victims reach out to object to their return.
A simple post explaining that they are being given a rare second chance, asking the community to respect their decision, and to come to you privately with any comments has worked wonders in the past.
@hawk is right in that the technology is only part of the solution, we have some members from some pretty incredible communities lurking here, learn from our (many many) mistakes!