The Leaver Game List
I came up with this idea while playing and dealing with leavers, of having an option to jump into games in progress to replace leavers. It would work by allowing leavers a certain amount of time to return (5 mins?) because of disconnects, after which the player slot they had would be put on the leaver games list.
The leaver games list would be the list of games currently in progress which have had a quitter slot which is up for replacement. You could search and sort this list by champion and game mode / time-in-game. When joining such a game you will take control of the abandoned champion they had with whatever skills and items but replace their runes/masteries/summoner spells with your own of course.
Why join a leaver game? Well because there would be an incentive. Not only would you perhaps be able to unlock special visual awards like banners and summoner icons for 'saving games' but players could also be rewarded with an increased chance of obtaining keys/chests. The perks could be worked out and refined later, but I personally would be happy to replace leavers for any incentive just for the good feeling of rescuing a game from being ruined by a leaver.
This may also eventually allow slightly relaxed penalties for leavers depending on how well the system works etc, broadening pardons for disconnects and other reasonable reasons for leaving early.
Please comment what you think! I know this would be a huge project for Riot, but I think it would be a HUGE positive change for the League of Legends experience and community. There is no way to ever eliminate leavers, so why not figure out a system for dealing with them?