The second chance is only for individuals who were banned for plagiarism and not for ban evasion cheaters, and anyone who plagiarised again would be banned again. This is simple.
I hope you are correct; that's the way it sounded in the OP but was a bit hard to tell for sure. Because once an account is un-banned for ban evasion, what's to stop them from getting re-banned in the future when another connection is made to their old (still banned) account?
Case in point:
This user claims they were banned for plagiarism but they were clearly banned for ban evasion: