Babylon relied on her sorcerers, magicians, necromancers and stargazers.
Nebuchadnezzars father, King Nabopolassar, had a slew of sorcerers, soothsayers, stargazers, diviners and wise men advising him of his every move. When King Nebuchadnezzar II took the throne, he inherited the mystic counsel from his fathers court. 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 the armies of Persian King Cyrus the Great, and King Darius the Mede, just as the Isaiah prophecy states. Not only did their gods fail to 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 had proved 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 fell lame. He was no match for the God of the Israelites. When the nobles and high priests removed the created idols that 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 by the Medes and Persians. Historical documentation, including the Cyrus Cylinder (539-538 BC) suggest that the city was taken without 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.