What is the test for deprivation of residual liberty under the writ of habeas corpus?

In certain habeas corpus cases an inmate can readily establish that there has been a deprivation of a residual liberty interest to which the writ of habeas corpus is available to review. Such situations would include, for example, if an inmate’s security classification has been increased or if the inmate has been placed in administrative segregation within the institution or sent to a special handling unit. (See: Mission Institution v. Khela, infra at para. 34). In those kinds of cases the real focus of the habeas corpus hearing is on whether the corresponding deprivation of residual liberty was reasonable and/or procedurally fair and/or within the jurisdiction of the decision maker.