They would see their houses burned before they fell by the sword of the king of Babylon. Ezekiel said to those princes:

“‘A sword you have feared, and a sword I shall bring upon you,’ is the utterance of the Sovereign Lord Jehovah. ‘And I shall certainly bring you forth out of the midst of her and give you into the hand of strangers and execute upon you acts of judgment.

Of course, these words show that Jehovah would really be the one executing judgment on these complacent schemers. But in doing so he would use the “sword” in the hands of foreign “strangers,” the Babylonians, to do the actual killing.