If you have to offer Sujud As-Sahw before the salam and you break wudu, then your prayer is rendered invalid. If you have to offer Sujud As-Sahw after the salam and you broke your wudu, then your prayer is valid and you do not have to do anything else.

It is prescribed to do Sujud As-Sahw in Nafl (supererogatory) prayers just as it is prescribed to do it in the obligatory prayers when there is a reason for doing it.