The Puppet Kings
A "puppet" can be defined as "a small figure of a person operated from above with strings by a puppeteer," or "a person who is used to perform unpleasant or dishonest tasks for someone else" (curiously, puppy and pupil originated from the same Latin word, pupa, as puppet). "Puppet governments" have long been established by imperial powers to give a conquered people the illusion of being free and sovereign. Ancient Israel, too, experienced it when they chose to go their own way, rather than continue in the LORD's Way.
"The king of Egypt made Eliakim his brother king over Judah and Jerusalem"
2 Chronicles ends with a list of the last kings of The Southern Kingdom of "Judah" (from which comes the abbreviation "Jew"). By that time, The Northern Kingdom of "Israel" had long-before become "the lost ten tribes" (see The Galilee Captivity) i.e. Israel was conquered and taken into exile by the Assyrians (see Ancient Empires - Assyria), then, over a century later (see Kings of Israel and Judah for approximate dates), Judah was conquered and taken into exile by the Babylonians (see Ancient Empires - Babylon). While all Jews are Israelites, not all Israelites are Jews (to understand about their coming future re-uniting, see The Gathering of Israel and Judah).
For the most part, the last kings of Judah were merely installed political puppets of the Egyptians (consider the irony of that, after the LORD had set them free from the Egyptians at the time of the Exodus), then the Babylonians. While Jehoahaz was obedient to the king of Egypt, he was "permitted" to be king of Judah; when the king of Egypt became displeased with Jehoahaz, he deposed him at whim.
"36:2 Jehoahaz was twenty and three years old when he began to reign, and he reigned three months in Jerusalem. 36:3 And the king of Egypt put him down at Jerusalem, and condemned the land in an hundred talents of silver and a talent of gold. 36:4 And the king of Egypt made Eliakim his brother king over Judah and Jerusalem, and turned his name to Jehoiakim. And Necho took Jehoahaz his brother, and carried him to Egypt." (2 Chronicles 36:2-4 KJV)
The king of Egypt replaced Jehoahaz with his brother Eliakim as "king" of Judah. Apparently a man of detail toward his conquered subjects, the king of Egypt even changed Eliakim's name to Jehoiakim (verse quoted above). The Lord had not only been allowing Judah's national subjugation and humiliation to happen, He actually made it happen because of Judah's gross disobedience toward Him. The Babylonians were then allowed to take their turn as the agents of God's wrath upon Judah and their corrupt kings, men who were blaspheming the ultimate King of Israel who will inherit that throne upon His return (see Israelite Monarchy - The Messiah).
"36:5 Jehoiakim was twenty and five years old when he began to reign, and he reigned eleven years in Jerusalem: and he did that which was evil in the sight of the LORD his God. 36:6 Against him came up Nebuchadnezzar king of Babylon [see also Nebuchadnezzar's Dream and Nebuchadnezzar's Conversion], and bound him in fetters, to carry him to Babylon. 36:7 Nebuchadnezzar also carried of the vessels of the house of the LORD to Babylon, and put them in his temple at Babylon. 36:8 Now the rest of the acts of Jehoiakim, and his abominations which he did, and that which was found in him, behold, they are written in the book of the kings of Israel and Judah: and Jehoiachin his son reigned in his stead." (2 Chronicles 36:5-8 KJV)
Jehoiachin, a child, was the next to briefly dance from Nebuchadnezzar's political puppet strings. Nebuchadnezzar soon thereafter replaced Jehoiachin with his twenty-one year old brother Zedekiah.
"36:9 Jehoiachin was eight years old when he began to reign, and he reigned three months and ten days in Jerusalem: and he did that which was evil in the sight of the LORD.
To his credit, Zedekiah rebelled against King Nebuchadnezzar, however it was too late. But Judah was not destroyed by the Babylonians; they were destroyed by themselves because of their evil behavior and refusal to repent after they were given fair warning by The Lord (see Why Babylon?).
"36:11 Zedekiah was one and twenty years old when he began to reign, and reigned eleven years in Jerusalem. 36:12 And he did that which was evil in the sight of the LORD his God, and humbled not himself before Jeremiah the prophet speaking from the mouth of the LORD. 36:13 And he also rebelled against king Nebuchadnezzar, who had made him swear by God: but he stiffened his neck, and hardened his heart from turning unto the LORD God of Israel. 36:14 Moreover all the chief of the priests, and the people, transgressed very much after all the abominations of the heathen; and polluted the house of the LORD which he had hallowed in Jerusalem." (2 Chronicles 36:11-14 KJV)
Fact Finder: Although not as well known, what prophet worked closely with Jeremiah at the time of Judah's fall to the Babylonians?