No. Once an account is validly permabanned it is gone for good, and not even pros or popular streamers have gotten any of their permabanned accounts back. Why? Because there has to be some lasting penalty and reminder that actions have consequences. From the Tribunal FAQ:
**Why can’t you give permanent banned players a second chance? You will receive a better player. **
Actually, this is the unfortunate problem. Allowing permanently banned players another chance is an extremely damaging cost. Do you know what the success rate of the Level 20 Challenge was? 5%. Do you know that for each person, they clearly outlined the toxic behaviors and had 1 on 1 conversations with the players to try to improve their behavior? These are players that were hand-picked by Player Support staff because they felt the pleas from these players were genuine. The success rate was still 5%.
Do you know how many games on average these players played? 100 games / month. When a permanently banned player fails to reform, they are creating miserable experiences for hundreds, maybe thousands of players a month. That's not a cheap cost or a low risk and we cannot consciously justify that, for the sake of the rest of our players.
These days players have at least 3 chances to reform (1 if given a 14-day ban for a zero-tolerance policy violation) before being permabanned, with the possibility of more if a player is able to improve their behavior before reaching that point. If that's not enough then Riot doesn't want you playing anymore. That said, Riot can't stop people from making new accounts, so if you truly want to prove you're reformed then do so on your other account. Oh, and before you or someone else tries to bring the money argument into this, to quote Kei143:
When Riot permabans someone, their philosophy is "the chances of this guy reforming isn't a whole lot, we'd rather not have him in the game". Thus in their eyes, they have already written off the toxic player as a paying client.
From a business standpoint, do they want to remove the toxic guy who has spent $500 but is causing a negative environment for 4-9 other players in every game? Those non-toxics are also spending $500 and probably will spend more, promote the game more when they are enjoying the game AND they won't cause a negative environment.
I personally think it is a fine argument to protect the ones that are paying money and aren't toxic rather than protecting the ones that may pay the same amount but are toxic.