there's nothing wrong but I guess it would sound much better if you could like put the subject like in this case "ellos" would take the place of "nadie" and you could say "nunca hacen nada" so nobody does anything, or follow by "y" like after you have already explained the issue can sound like frustration " ...y nadie nunca hace nada". and still it doesnt' sound good to me you know what instead of saying "Nunca" you could say "siempre es lo mismo" something like "nadie hace nada,siempre es lo mismo" there you go...

Your sentence is absolutely correct. Perhaps you think is wrong because someone told you than the adverb can't be said before the verb, but it isn't true. You can play with the order of the words, to give emphasis to one or another of the ideas. 1.- "Nadie nunca hace nada". Emphasis on the subject, "nadie" is the most important idea you want to accentuate, and "nada" the second one. 2.- "Nunca nadie hace nada". You want to give emphasis to "Nunca". Anothers options....Nadie hace nada nunca, nunca hace nada nadie , nunca hace nadie nada...

La oración -Nadie nunca hace nada- es correcta.