Suppose you were a minor Babylonian noble resident in the city when the Assyrians took the city in the 13th century BC. What (if anything) would happen to you?

A key factor to consider in this case is that, while the Assyrians seem to have garnered a reputation for being physically brutal, the reality is in fact rather more nuanced, with psychological warfare being a popular tactic of subordination as well. Tikulti-Ninurta I's seizure of Babylon in the 13th c. BCE coincides with the first known incidences of mass deportation, a strategy that would continue through the Neo-Assyrian Empire as well.

The reasons behind these deportations were numerous. First and foremost, forced relocation preserved human lives-- valuable resources to preserve the Middle Assyrian economy. Removing individuals from their native homelands had an added effect of psychological upset, with the possibility of splitting families being enough to encourage most new Assyrian "citizens" to toe the line. Finally, planned relocations had the potential to homogenize the ethnic makeup of Assyrian society, creating a new, multiethnic identity.

In spite of their hierarchal stature, it would seem that élite residents of Babylon would have been no exception. The textual record-- left to us courtesy of Tikulti-Ninurta I-- indicates that the deposed king, Kaštiliašu IV, was brought to Aššur as a political prisoner. Although my intuition is that his ultimate fate upon arrival was rather unpleasant, this does indicate that Tikulti-Ninurta I understood the value of public subjugation and embarrassment for the upper echelons of Babylonian society.

Therefore, it is most likely that a Babylonian noble would be stripped of property and connections through the nascent deportation program. There may have been some potential to climb the ranks of Assyrian society by rebuilding connections and serving the new king well, but as the conquered people, it is hard to ascertain what became of most deportees.

If you are interested in further relevant reading concerning this subject exclusively, I can certainly root around and try to locate some article recommendations. Unfortunately most new archaeological material concerning this subject completely lacks provenance due to the state of the black market for cuneiform tablets of late. For a quite broad/general discussion of the deportation system in the context of history, however, a great place to start would be Amélie Kuhrt's The Ancient Near East.