An advanced form of Rage Quitting. When a player ragequits, they simply give up and abandon the game, normally not firing anymore than a profanity here or there.
When they trollquit, however, they intend to do as much damage as possible to the players in the game on their way out. They do this by declaring wars and in general causing chaos. These actions are generally unfeasible from a real world standpoint. For example, using nuclear weapons on a nation for no reason is generally trollquitting, whereas using nuclear weapons when one is about to be finished is generally not.
A common trollquit takes the form of players having built up a massive arsenal of WMD (which has become common since the taboo was broken in IOT IV) and, upon the game no longer going their way, firing them at whoever has annoyed them, or failing that, everybody. Trollquitting is generally successful, as it tends to devastate many player nations and causes large amounts of rage.
Some textbook examples of trollquits can be found in Sons of Mars 3 - when Double A's invasion of Byzantium and Greece was thwarted, he responded by firing everything in his arsenal at nations that annoyed him. Later in the game, Red_Spy's nation of Partitionania amassed an arsenal of the biggest, most deadly WMD imaginable and destroyed half of the rival nations of Germany and Russia out of simple boredom. In Multipolarity, Red_Spy once more attempted a nuclear ragequit, destroying several Comintern nations, though hilariously not landing a single missile against Coruscant. Another infamous example was in Imperia Mobiana, where the GM - TaniciusFox - actually broke his own rules (though he made a retcon so that he did not) to end the game quickly; this is the source of the Enerjak meme amongst IOTers.
Some GMs, however, have become aware of the dangers of trollquitting, and have made limits on such. Sonereal, for instance, has stated that trollquitting will result in being blacklisted from future IOTs or, failing that, face penalties on WMD development in future games.