What condition occurs when a form of bilirubin diffuses into the brain and causes a type of encephalopathy?

This condition is called kernicterus or bilirubin encephalopathy.

Kernicterus is a condition when unconjugated hyperbilirubinemia occurs, (for example, as a result of hemolytic disease). As a result, unconjugated bilirubin crosses the blood-brain barrier and, because it is lipid soluble, it penetrates neuronal and glial membranes. It usually happens in the neonatal period and prematurity and low birth weight are the major risk factors for bilirubin-induced brain injury.