But why would anyone invest in stocks under the scenario he describes? The idea that if I invest $1 in the wrong company may mean that I lose my home and everything else I own simply means that I won't be investing in the market. Period.
Imagine the case of someone with all their money in index funds, I would now be liable for EVERY SINGLE PUBLIC COMPANY. People would flee the stock market so fast it WOULD go to near 0.
No, the key is to threshold it so it only applies in the extreme cases.
For example, let's say, bankruptcy only lets you discharge 100% of the first $1 trillion. After that, some combination of owners/officers/executives are responsible for (say) 0.1% of obligation beyond $1 trillion.
With these thresholds, it hardly applies to "every single public company".
This makes absolutely no sense. Have any of these companies racked up losses beyond $1 trillion? And even if they have, who is going to pay for the other 99.9% of their losses? This makes no difference to anything, except that you're now making some investments too risky for anyone to touch. The key, however, is not that the super-risky investments are the ones where companies look risky. They're just ANY company in certain industries.
So you wouldn't invest unprotected. Insurance was invented to solve this specific problem: socializing the costs of unlikely but disastrous occurrences.
The vast majority of companies will be fine the vast majority of the time, so there's plenty of opportunity for an organization to sell inexpensive insurance which covers for those rare cases where the pot boils over.
What you're suggesting sounds suspiciously like AIG and the whole "credit default swaps" mess. What about when the insurance company goes under and needs a bailout?