Naevia struggles to breathe. She has a hacking cough that sprays phlegm in your lap. And you think you're onto a sure thing? You've missed the point, Bithynicus: Naevia isn't dying, she's leading you on.
The greedy legacy-hunter, solicitously paying court to the elderly and sick (and childless) in the hopes of a generous bequest, is a fixture of Roman satire; Naevia knows exactly what Bithynicus is up to, and is milking the situation for all the attention and goodies she can squeeze out of him. The player, played.