Problem is not whether they emit VOCs after some time (they certainly do), but whether the amounts they emit is harmful.
And the answer is: it depends. On the maker (large, international firms usually follow regulations to avoid legal troubles, small firms are sometimes even not aware any regulations exists), on the market (things sold in EU will be definitely much, much safer than the ones sold in, say, middle Africa), on the item (nail polish is used in very small amounts, so the amount of solvents and other chemical is quite low, furniture weights many kilograms and can contain quite a lot of VOCs.