The word scavenger comes from an old term for someone who cleaned streets and collected waste. Today it means a person or animal that searches for and gathers discarded or leftover items.
Read the question again: a person who searches for and collects discarded items. The action described is searching plus collecting, and the object is discarded items. This is the exact job of a scavenger.
Pauper, beggar and bankrupt all describe a person's financial condition, not an activity of searching and collecting. None of them can replace scavenger in this sentence.
So the one word that stands for the whole phrase is Scavenger, which makes option A correct.