Tennessee Code Title 20. Civil Procedure § 20-1-111

(a) Where one (1) of several executors or administrators removes out of the state, actions may be prosecuted and judgments rendered against such as remain, in the same manner as if all were sued.

(b) If the cause of action is within the jurisdiction of a judge of the court of general sessions, it may be prosecuted against the administrator or executor who remains in the county, where one (1) of them removes out of the state or into another county.