What is the fate of micronucleus DNA?
Emergence of Micronuclei and Their Effects on the Fate of Cells under Replication Stress (2010) explores how micronuclei behave and determine cell fate. It found that micronuclei is pretty closely related to apoptosis. If the cells with micronuclei didn't go through apoptosis, there were instances where the micronuclei would literally just disappear. They were unable to determine if it was expelled by the cell or reabsorbed into the main nucleus. However, there were also cases where there would be an increase in the number of micronuclei. 

They concluded that there is a number of ways for the cell to get rid of the micronuclei and they were unable to determine which is the most likely.

I was unable to find any more recent in-depth studies (that I could understand).



So, according to this paper there are several answers...


Case 1: It is reabsorbed into the nucleus and most likely the information within is saved.
Case 2: It is expelled from the cell and the information within is lost.
Case 3: The cell undergoes apoptosis and all information is lost.