Albert Barnes Commentary Jeremiah 29:1

"Now these are the words of the letter that Jeremiah the prophet sent from Jerusalem unto the residue of the elders of the captivity, and to the priests, and to the prophets, and to all the people, whom Nebuchadnezzar had carried away captive from Jerusalem to Babylon," — Jeremiah 29:1 (ASV)

The residue of the elders – that is, the elders who were still alive.