I think it's not correct. It should be an adverb, sole. Otherwise it's: The lonely Corinna lives.
I am by no means a Latin expert, but I find that Latin writing often uses adjectives as adverbs whenever they could theoretically be describing the subject in addition to the verb itself. I usually switch these adjectives to adverbs or dislocate them when translating, but you could also insert a "the" as you did. That approach would be awkward for this sentence but works in a sentence like "Livia irata respondit" which literally translates to "*Livia angry responds" but could also be translated as "Livia angrily responds" or "The angry responds" or "Angry, Livia responds". It should also be noted that, to my knowledge, "solum -a -us" does not necessarily mean "lonely" in the sense that Corinna is depressed, it just means that she is alone. I see what you mean, though. "Lives alone" is somewhat idiomatic, so the grammar breaks down there when translating. Good catch.</pre>
Latin usually has adjectives (not adverbs) when describing a spatial or temporal relation; solus belongs in that category (alongside e.g. primus 'the first' or ultimus 'the last'). There's the adverb solum, but you will find that mostly used non solum ... sed etiam ('not only ... but also') and variants.
It's -e for nouns, but with adjectives its the ending for an adverb. But in this case sole wasn't used in classical Latin. So sole is not the answer but Corinna sola isn't the answer either.