Adjectives and verbs can be transformed into nouns. To transform a verb into a noun, add "-ing" to produce a gerund. For an adjective, just add "the", as you observed. Note that "a" or "an" do not suffice for this purpose. You can't say "a poor". You'd have to say "a poor person". Past and present participles, since they function as adjectives, can also be treated this way. Verbs can also be used as nouns in their infinitive form: "I like to sing".

The simple answer is yes. A past participle can be an adjective so it’s the same thing. The poor face many problems.