Abuse of power does not only happen when evil leaders act out of self-interest, but also when good leaders fail to do what they should do. In this case, King Zedekiah delegated an unwanted task to someone else and declared himself unable to act. The king lacked the courage to use his power to protect the prophet.
Jeremiah, on the other hand, remained committed to a mission he did not enjoy. He proclaimed the destruction of his own people and named Babylon as the one who would carry it out. Imagine you were an evangelist standing in church today, proclaiming that God is raising up the communists to punish Germany. You declare that God doesn't care about reunification or the constitution. It even goes so far that the message you're emphasizing seems to offend God. Yet when you try to stop speaking this message, you feel disobedient. The word burns within you, and you have to speak it. So you take on the responsibility and don't go looking for popularity. That was the man, and that was the message, of Jeremiah.
Jeremiah 38:1-6
Jeremiah in the Dungeon
1 Then Shephatiah the son of Mattan, and Gedaliah the son of Pashur, and Jucal the son of Shelemiah, and Pashur the son of Malchiah, heard the words that Jeremiah had spoken unto all the people, saying,
2 Thus saith the LORD, He that remaineth in this city shall die by the sword, by the famine, and by the pestilence: but he that goeth forth to the Chaldeans shall live; for he shall have his life for a prey, and shall live.
3 Thus saith the LORD, This city shall surely be given into the hand of the king of Babylon's army, which shall take it.
4 Therefore the princes said unto the king, We beseech thee, let this man be put to death: for thus he weakeneth the hands of the men of war that remain in this city, and the hands of all the people, in speaking such words unto them: for this man seeketh not the welfare of this people, but the hurt.
5 Then Zedekiah the king said, Behold, he is in your hand: for the king is not he that can do any thing against you.
6 Then took they Jeremiah, and cast him into the dungeon of Malchiah the son of Hammelech, that was in the court of the prison: and they let down Jeremiah with cords. And in the dungeon there was no water, but mire: so Jeremiah sunk in the mire.