Am not an attorney in Tennessee. However, there usually are immunity statutes respecting inmates and liabilies for injury caused by them to others. By immunity, I mean the law says that you may not sue the government. You may sue the inmate responsible, but I doubt you would obtain much.
Rarely would such a case against a governmental unit be successful.
This answer is offered for informational purposes only. It is not offered as, and does not constitute, legal advice. Laws vary widely from state to state. You should rely only on the advice given to you during a personal consultation by a local attorney who is thoroughly familiar with state laws and the area of practice in which your concern lies.
From a strictly legal standpoint, there is the possibility of bringing an action against the governmental entity for the failure to properly supervise.
From a practical standpoint, it is going to be very difficult to find an attorney willing to take this case. I am afraid a jury would not be particularly sypathetic to this cause of action. It is my experience that it is very difficult for an inmate to sue the prison system successfully, as jurors often are not willing to compensate an inmate, unless the facts are absolutely crystal clear.