Jeremiah 50:3

An invader would descend on Babylon from the north and would make her an object of astonishment. All of Babylon’s inhabitants, humans and animals, would leave her. Elsewhere in Jeremiah the enemy from the north is Babylon, but in the future, ironically, the invader of Babylon itself would come from the north.

"The reference at this stage is hardly to the Persians who came from the east, although the strategic line of attack was roughly from the north." [Note: Thompson, p. 733.]

Neither was the land, or even the city, totally uninhabited after the Persians took over. People did not flee because of the Persians. For example, Daniel, who had access to Jeremiah’s prophecies (Daniel 9:1-2), remained in the capital city during and after its fall (Daniel 5:28; Daniel 5:30-31; Daniel 6:1-3).

"Several times Jeremiah repeated this fact about Babylon being without any inhabitants (cf. Jeremiah 50:39-40; Jeremiah 51:29; Jeremiah 51:37; Jeremiah 51:43; Jeremiah 51:62). The city was spared and made one of the ruling centers for the Persian Empire with Daniel serving there in an administrative position (cf. Daniel 5:30; Daniel 6:1-3)." [Note: Dyer, "Jeremiah," p. 1199.]

Alexander the Great destroyed Babylon in 330 B.C., but that destruction was not from the north, or final, either.