Honestly I don't know you would have to send a support ticket, I just got perm-banned because I went on Tilt, I got forced into a bot role like 3-5 games in a row, had an AFK during champion selection, and my bot lane refused to play defense when it was called at champion selection, as a result " I Did feed hard" not Intentionally but "Riot decided to issue a perm-ban for doing this.
I submit two support tickets, and Riot keeps giving me the same responses of being Audited, but honestly I find no real way to appeal these type of bans, and I say this being 3-4 year old League Player at least there is no way I would Intentionally feed despite doing awful.
Like with all honestly I could just Open a new account, but with the current forced role system even if I dumpted $700 Into the game and bought everything back I lost, I would just get banned for Intentional Feeding again for doing awful all over again I did this bad before.
As far as having a ban removed if you were indeed toxic in chat is a different story, I don't know if Riot is willing to do this I know they have given some pro players a chance to improve their behavior though, and I would like to be given a chance to prove I don't Intentionally Feed to get my account back, even if it takes playing a few months on a new account with the new role system which I know I can play better in compared to forced roles.
Yes Perm-Bans can be undone.
Riot just doesn't want to or they believe in their auditing / statistics system more than they believe or trust its players, and I agree some perm-bans are deserved but some of these bans that I see being handed out lately I would have to question.