permanent ban

What does "permanent" even mean? Come on, common freakin' sense.

If they can prove that the mistake was on Riot's end then yes, they will be unbanned.

They are very rare but they do happen if you can prove your account was stolen or provide decent evidence that the account was banned by mistake.

Hey, I have a helpful link for you.

http://lmgtfy.com/?q=definition+of+permanent