这个句子如果改为主动句,则requiring动名词短语为主语。在被动句中,原来的主语由介词by引出,by介词短语在被动句中属于方式状语。
requiring them often to pay damages to those unlucky enough to be hurt working for them. 在这个动名词短语中,them为动名词的宾语,often to pay…为宾语补足语。
those=those people, unlucky enough to be hurt working for them整体是形容词短语作those的定语。形容词unluck被enough to do副词短语修饰。其中
to be hurt working for them为不定式短语修饰enough,为enough的结果状语。working for them是不定式to be hurt的时间状语,是不定式短语的内部结构。这个句子如果改为主动语态则为动名词短语作主语:
Requiring them often to pay damages to those unlucky enough to be hurt working for them should not slow the progress (that) railroads represented.