down-and-out vs poor person

down-and-out and poor person both are nouns.

Word	Noun	Adjective	Verb	Adverb
down-and-out	Yes	Yes	No	No
poor person	Yes	No	No	No

As nouns, poor person is a hypernym of down-and-out; that is, poor person is a word with a broader meaning than down-and-out:

Other hypernyms of down-and-out include have-not.

down-and-out (noun)	poor person (noun)
a person who is destitute	a person with few or no possessions

down-and-out (adjective)	poor person (adjective)
lacking resources (or any prospect of resources)