"That Corinna sings sweetly."
Translation:Illa Corinna suaviter cantat.
I believe this is not commonly used. See "this thing" vs "thing, this" in English for example, so the determiner comes before the noun.
I don't know how often romans used appositions, perhaps not at all, but this is just how it would look like: Corinna, illa puella (haec puella non est), suaviter cantat.
"That Corinna" is just pointing out that the subject is that one, far from the speaker, and not this one, nearby.
In my view, iste/ista suddenly alone in fact sounds like treating the subject as any object rather than a being, like saying "this one" in english, and mostly any other language.