People ask for the original email and the copy of the first message you get from riot when you register a new account, since that`s the main evidence that you need to provide to the riot support that you are infact the owner of the account so you can recover it. Ofcourse that`s not enough to recover an account though.
To answer you last question: No, there is no way to make an account unrecovarable as to i know, it`s up to riot`s support specialists to decide wether to give the account back to the one claiming in the ticket it`s his, or to avoid returning it. Ofcourse they make a deep investigation such as IP checks, old log-in logs ect. So there is no 100% chance that the second owner of the account would get it back, nor does the original creator, since he might not have all the information requiered to recover the account. So overall recovery is based on the information you posses of the account and if it checks out, also it deppends on the decision of the riot games specialists.