Depending on the virus, a variety of genetic changes can occur in the host cell.  In the case of a lytic cycle virus, the cell will only survive long enough to the replication machinery to be used to create additional viral units.  In other cases, the viral DNA will persist within the host cell and replicate as the cell replicates.  This viral DNA can either be incorporated into the host cells genetic material or persist as a separate genetic vector.  Either case can lead to damage of the host cells chromosomes.  It is possible that the damage can be repaired; however, the most common result is an instability in the original genetic material or suppression or alteration of the gene expression.