- You may also be looking for political asylum.
An asylum was a type of psychiatric hospital designed to care for, maintain or cure the mentally ill, or mentally insane. They differ from penal colonies, in most cases, because the basic intent of the facility is to actually help cure the criminally insane rather than merely detaining them or forcing them to perform labor as their retribution.
During the late 23rd century, the Federation maintained a handful of asylums for the "few remaining incorrigible, criminally insane of the galaxy." One such asylum was maintained at the Elba II colony on the planet Elba II. (TOS: "Whom Gods Destroy")