Tennessee Code Title 21. Proceedings in Chancery § 21-1-203

(1) When the defendant is a nonresident of this state;

(2) When, upon inquiry at the defendant's usual place of abode, the defendant cannot be found so as to be served with process, and there is just ground to believe that the defendant is gone beyond the limits of the state;

(3) When the sheriff makes return upon any leading process that the defendant is not to be found;

(4) When the name of the defendant is unknown and cannot be ascertained upon diligent inquiry;

(5) When the residence of the defendant is unknown and cannot be ascertained upon diligent inquiry;

(6) When judicial and other attachments will lie, under this code, against the property of the defendant; and

(7) When a domestic corporation has ceased to do business and has no known officers, directors, trustees or other legal representatives on whom personal service may be had.