Ah, this is a nice touch by Twain.
The first time Twain mentions this, he just says that Emmeline Grangerford "took sick." However, within a page or two he turns this into a nicely sarcastic touch, having Huck tell the reader that Emmeline "pined away" after she couldn't find a rhyme for a deceased person named "Whistler." She died, in other words, of poetic frustration!
She was killed not by any diseases or humans, but by disillusion and hysteria about poetry confusion and utter madness. She couldn't find a rhyming word for a dead person, called "Whistler" and that take a toll over her physical and mental being and brings about her untimely death.