Albert Barnes Commentary 1 Kings 13:34

"And this thing became sin unto the house of Jeroboam, even to cut it off, and to destroy it from off the face of the earth." — 1 Kings 13:34 (ASV)

This persistence in wrongdoing, after the warning he was given, brought judgment not only on Jeroboam himself but also on his family. Jeroboam’s departure from the path of righteousness forfeited the crown (1 Kings 11:38), and this forfeiture naturally involved the destruction of his family.

In the East, as has already been observed, when one dynasty supplants another, the ordinary practice is for the new king to destroy all the males belonging to the house of his predecessor (see 1 Kings 15:29).