I would say, "hanging loose." "Hanging loose" means disconnected, not fastened or secured in place. "Hanging loosely" gives me an image of draped cloth or an outfit that is too large for the person wearing it, so it hangs loosely.
More troubling than the question of whether to use an adjective or an adverb here is the meaning of the sentence itself. I have no idea what the writer could mean when suggesting that sentences are "not properly connected." Generally, sentences in a paragraph, say, are connected by topic and focus, not grammar.