Babylon relied on her sorcerers, magicians, necromancers and stargazers.
Nebuchadnezzars father, King Nabopolassar, had a slew of sorcerers, soothsayers, stargazers, diviners and occultist advising him of his every move. When King Nebuchadnezzar II took the throne, he inherited them as part of his counsel from his father. But Nebuchadnezzar found that only the God of Israel could reveal secrets, and was true to His Word.
The ruling elite of Babylon were deeply humbled when their false gods, sorcerers, diviners and stargazers were unable to warn them of the invasion of King Darius and the Persian King Cyrus the Great, just as the Isaiah prophecy states. Not only did their gods not warn them, but those idols held them captive, promising peace and security from within Babylon's massive walls.
What a burden their idols became for them. Neither Bel or Nebo could stand erect on their own. The Babylonians hauled them away in their wagons, as they had no use or power of their own. The God of Israel has shown them that their golden idols of pagan gods, and carved animals were a heavy burden, mute and of no help. Even Marduk the Snake-Dragon – chief god of Babylon had been muzzled and lame. He was no match for the God of the Israelites. When the nobles and high priests removed the created idols that had failed them, they became a heavy burden under the victorious God of Israel.
The Isaiah prophecy has more spiritual meaning than a physical one with the lackluster and worthlessness of the pagan idols.
There is no mention of the people scattering or fleeing Babylon after the conquest of the Medes and Persians. Historical documentation, including the Cyrus Cylinder (539-538 BC) suggests that the city was taken without much of a fight. In fact, the inhabitants of Babylon were not even aware that they had been captured: Daniel 5. Only the elites and their concubines were aware of the siege. Thy kingdom is divided and given to the Medes and the Persians.