Most of the punishments are handled by the Instant Feedback System (IFS) except for AFK punishments (which are handled by the Leavebuster System). Unfortunately, it's much harder for the system to detect intentional feeding because it is tuned to prevent itself from handing out liberal punishments to players who might have just been having a bad game. However, players who are intentionally feeding and/or trolling are punished much more severely. Usually, the first punishment for verbal abuse is a chat ban but the punishment for intentional feeding (even if it was your first offense) is a 14-day ban.
If you had someone in your game who you believed was intentionally feeding, I'd recommend you download the replay, convert it to a format that you can upload to YouTube and then send the link in a report ticket on Riot's Support webpage. It sucks because it can take some work, but it's the best way to make sure that an intentional feeder/troll gets punished.