After the end of the Pacification Campaign, they dropped out of the ISC because its people no longer supported the bloodshed the Council of Five generated in the name of the Declaration of Ideals. They spent the following 80 years or so trying to distance itself from the ISC.
The Korlivilar Consortium was the government of the Korlivilar people. It was torn by a civil war in 2384 caused by a crime wave whose roots trace back to their version of World of Warcraft. (RIS Bouteina: "Declaration of Warcraft")
After the disaster of the Pacification Campaign, the Korlivilars maintained a fleet of starships, but only for peacekeeping purposes rather than for war. As such, they tried to reserve violence to holodecks and other virtual environments as much as it was possible. (RIS Bouteina: "Declaration of Warcraft")
The name used in the RIS Bouteina episode Declaration of Warcraft is the name of the species in Rihannsu whereas the race called the Korlivilar in English is in the same family as the Lyrans (and also a member species of the ISC), even though they are not from a common stock.