Tenn. Code Ann. § 29-6-146: Notice mailed to nonresidents

(a) Where publication is made for a nonresident defendant the clerk of the court, in which such suit is filed, shall, immediately after the first publication, mail a copy of the newspaper containing such publication to each of the nonresident defendants directed to each nonresident defendant's last known place of residence, if such place of residence is known or can be ascertained upon inquiry.

(b) The clerk shall make an entry thereof upon the rule docket showing that such notice has been mailed, for which the clerk shall receive a fee of twenty-five cents (25¢), to be collected by the clerk as other costs in the case.

(c) Any failure of the clerk to give such notice shall not invalidate or make voidable any proceeding in court against a nonresident defendant.