Sometimes a mind flayer that's away from its colony breaks free from the elder brain. Perhaps it ran into a situation where its bonds of obedience were broken, or perhaps the colony was destroyed while it was away. In such a case, the mind flayer becomes free-willed for as long as it avoids contact with an elder brain.
A renegade illithid remains fearful of gith attacks, and likely sets about creating a sort of colony of its own, the better to remain undetected. It gathers minions, establishes a lair, and makes defense of its territory a top priority. Unlike colonial mind flayers, rogue illithids develop a healthy respect for those not of their kind. They treat especially powerful creatures and individuals as equals, not adversaries, and seek to cooperate with them. A renegade mind flayer might become a trusted advisor or a powerful ally, so long as it is kept well fed. Any alliance it makes, however, collapses if the mind flayer falls under the sway of an elder brain once more.