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.
