When a person confined in a penal or correctional institution or reformatory of this state is evaluated as provided by law by a licensed mental health professional to be a person requiring treatment as defined in Section 1-103 of this title, the district court may order the inmate's transfer to a facility, or unit within the Department of Corrections and make a determination of whether the inmate is capable of consenting to or refusing treatment that is ordered including, but not limited to, the right to refuse medication, pursuant to the laws governing involuntary commitment, where the inmate shall remain until the person in charge of the correctional institution or unit, or the physician which received the inmate determines that the inmate has improved to the point that the inmate may be discharged pursuant to the laws of this title governing discharge. If the sentence expires during the time of a prisoner's involuntary commitment at the correctional institution, and the prisoner is still a person requiring treatment, the person in charge of the correctional institution shall immediately instigate proceedings for commitment to the custody of the Department of Mental Health and Substance Abuse Services or to a private facility willing to accept the person for treatment under the procedures provided in this title.