定语从句修饰名词或者代词。在你的句子中，（that）the most costly and dramatic measure may be painful 的前面没有名词或者代词，而是及物动词know，所以（that）the most costly and dramatic measure may be painful 是宾语从句，其中the most costly and dramatic measure是从句的主语。
I know the most costly and dramatic measure （that）may be painful.你可能把这里的may be painful误认为是定语从句了。如果是定语从句，作主语的关系代词 that 是不能省略的，只有作宾语的关系代词才能省略。
