The answer is “YES”, although the circumstances have to be extraordinary. Globally, only a few markets have gone to zero. The largest was Russia in 1917 and China in 1949. While other markets have collapsed, they have subsequently recovered.
The stock market is a reflection of the overall economy and while it may experience turbulence in the short-term, going to zero is extremely rare. For the whole stock market to go to zero, every company would have to be bankrupt, and this will (probably) never happen.
The stock market often feels irrational, but in its own way it is the ultimate barometer of public sentiment. As horrible as it sounds, the stock market cares about profits, not democracy. I should point out that if this happens, “guaranteed” investments such as FDIC-insured bank accounts and government treasuries will also be valueless, and even if you held “safe haven” assets such as physical gold, you would not be able to protect it.
If you diversify your investments beyond just the US stock market, and also include the global stock market, the chances of your investments going to zero are too remote to warrant consideration. This sort of thing shouldn’t keep you up at night.