Usually called upon to clean up a mess another mobster has made. For instance: a gangster robs a store one night and comes back to base with a bullet in his stomach. A cleaner is quickly called-up and will be sent in to clear any sight of evidence, even if this means killing the store-keeper.
Elite cleaners are rarely found in the mobs/mafias/gangs etc., but instead apart of a government agency. Considering the drastic consequences often involved with these agencies actions, elite cleaners are required. You never hear of them, and you rarely hear of what they have cleaned up. All that's left is the event: something happened, but the cleaner will make sure there are no trails left behind. Such cleaning jobs can be on a global scale, such as clearing a trail of money used to get the job done.