On The Estate of Apollodorus (30)

All men, when they are near their end, take measures of precaution on their own behalf to prevent their families from becoming extinct and to secure that there shall be someone to perform sacrifices and carry out the customary rites over them. And so, even if they die without issue, they at any rate adopt children and leave them behind. And there is not merely a personal feeling in favor of this course, but the state has taken public measures to secure that it shall be followed, since by law it entrusts the archon with the duty of preventing families from being extinguished.