I can't speak for all alternatives, but for "rik" it only applies to definite form (den rike/rika, de rika), but it doesn't work in the indefinite any more than "a rich" works in English. Just like the English equivalent, you'd replace it with "en rik man" (a rich man), "en rik kvinna" (a rich woman), or any other noun of your choice.
It's a pretty big grammatical category, 'adjectival nouns', in Swedish ett substantiverat adjektiv. We simply take an adjective and use it as a noun. You do in English too, when you say the poor in 'give to the poor' for instance. 'An adult' is en vuxen.
I used an article because I translated what Laski-Julle said, The adults, but de vuxna is just the determinate form of vuxna. The sentence on top here is about adults in general so we don't use an article, but if we wanted to say about some specific adults that they're crying, it would be The adults are crying in English and De vuxna gråter in Swedish, so it works the same way.