They won't lose the force-placed business. It is something that the mortgage market requires in order to function properly. Their margins in this could be hurt, but, as they say, all of their rates have been approved by regulators, so I wouldn't expect huge price reductions.
Rates may be approved by regulators, but that doesn't shield AIZ from new competition. All it takes is some smaller writers to begin pricing the product closer to true historical loss costs, and the market share for Assurant (and QBE) will get hammered. It is politically expedient and consumer friendly for both elected officials and insurance commissioners to push for lower rates.