I actually have a pretty good idea what this is about. Head over to any sketchy account market or eBay seller offering $5.00 accounts and you'll notice a trend. They all have a disclaimer that the accounts are "inactive with unverified emails" or something to that effect. What this means is that someone either guessed an account's password because it was obvious, common, or had something to do with their account/summoner name. These accounts are then stolen and, because it took very little time to steal the accounts as opposed to botting them to level 30, they are sold for very low prices.
Anyway, people buy those accounts cheap and then end up unable to log in a few days later. Either because the original owner found out (possibly through their friends list since surprisingly enough, it seems like wiping a stolen account's friends list isn't the standard) and changed their password, or because the seller/thief sold it to multiple buyers and one of them figured out a way in to the unverified email account. From my understanding, the seller will often use any RP/IP on the account to make it less identifiable (including using name changes).
In the end, the account owner usually gets their MMR tanked (or boosted if they're lucky) and eventually gets their acount back. The buyer basically just gets screwed, as they aren't getting any help from Riot (account sharing/selling is against the TOS) and the vague disclaimer seems to cover the seller enough. Many scam artists on eBay in particular seem to operate from long standing accounts with exceptional reputation ratings, begging the question; "Were they stolen as well?"
It's a cut throat business and, in the end, only the seller comes out on top. I couldn't begin to delve in to how many accounts are stolen/resold this way, however, if I had to hazard a guess, I'd place that number in the tens of thousands.
Moral of the story: Use a safe and secure password not only for your account, but your email as well.