Albert Barnes Commentary 2 Kings 16:6

"At that time Rezin king of Syria recovered Elath to Syria, and drove the Jews from Elath; and the Syrians came to Elath, and dwelt there, unto this day." — 2 Kings 16:6 (ASV)

Either during the siege or after withdrawing from Jerusalem, Rezin made an expedition to the Red Sea coast and took control of the city, which had belonged to Judea for about 70 years (marginal reference). Most modern commentators render this verse as: “Rezin recovered (or restored) Elath to Edom... and the Edomites came to Elath.” Regarding the resemblance between the words Aram and Edom in the original text, see the note on 2 Samuel 8:12.