Your new account is your second chance. You'll also get a third chance, and a fourth chance, and a fifth chance and so on, since they can't do IP bans without collateral damage and it'd be difficult to associate your new account with you unless you were a streamer or in some other way indicated you were the owner of the new account. You'll have to start over from scratch every time you get another chance, though.
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Riot doesn't typically unban permabanned accounts because otherwise the permaban wouldn't hold as much weight. The idea with the escalating punishment system is that if you don't learn from the chat restrictions and temporary bans, then a permaban is the next step and a permaban is well permanent. You're given an opportunity to learn from your mistakes and stop BEFORE the permaban.
Sometimes you don't get a chance to learn from your mistakes because they escalate immediately to a permaban.