Based on a recent experience I had with nail polish, yes, I do believe it can go off.
Only recently I received (well purchased I suppose) a small bag of makeup goodies from a garage sale/charity type thing where at the end of the day they were trying to get rid of them and I donated a token amount for it. Within that bag, well, the makeup wasn't all that magnificent but there were one or two things that were worth it.
Inside was an Avon nail polish, or rather 'Nail Soother' which I was quite curious about. The chunky, angular bottle with the gold topped cap looked rather classy and had it not had 'Avon' written all over it, I would have presumed that it was of a more expensive brand.
Anyhow, as soon as I opened it there was a foul smell. It was so strong and potent. I don't know what possessed me to put it on my nail, but it was very much a failure anyway. Much like oil in a fry pan, rather than a thin layer coating the nail evenly, it drew back into 'blobs' that sat on the nail and slid around all over the place. What on Earth?
I haven't even experienced anything like this before, but can nail polish go off? No just separate of change colour a little, I mean really go off!