They already get downsides if company gets fines or even goes to bankruptcy. You never know whether they invested based on information that was not true at all. Which is unfortunately too common.
There is literally no way to have the broad base of investment in markets by members of the public that we see today if investors incur personal liability. It was and remains one of cornerstones of any commercial society.
Let's say the investor part doesn't apply to public companies, to make it simple.