LLC's are state inventions, and thus vary quite a bit, but one standard feature is that you can't be liable for more than you put in. Thus they are shielded from any excess liability beyond their investment. This is true of c-corps today for sure.
However, on top of that, they usually have almost no formalities or regulations, making piercing the corporate veil incredibly difficult.
C-corps have limited liability (now), but piercing is much easier for bad acts, and they have lots of regulation and formality (historically) that helped prevent bad acts in the first place.
The LLC changed a lot here - you could form businesses basically structured any way you want, with almost no regulations, and still not be liable. Outside of constructing an LLC to do totally illegal things (like rob banks or something), you and your shareholders are pretty much never liable.
That is definitely not true of C-corps, and was even less true historically :)
For limited liability in general:
General forms of limited liability are about 100-150 years old, depending on country.
IE before 1850, it was pretty rare. I believe new york has an earlier statute, but it was uncommon.
LLC's are not corporations, either, under most state law, they are special forms of companies.
The alternative mind you, was sometimes double liability for shareholders, who both lost their investments, and had to pay for excess loss.
I'm actually okay with that - it's a good way to ensure better diligence and less risk.
It's true that LLC's enabled innovation that would have been slower, but at a tremendous cost - enabling almost any risk to be taken for free is to me, a lot worse than slower innovation. It also lead to totally perverse things (toxic dumping, etc) and shareholders didn't worry or care because at most they lost some of their investment, and most of the time, could easily pull it out before the shares dropped, and move on to investing in the next horrible thing. In the old world, they would have been responsible for the entire cost, even if they pulled out.
Limited liability is a bad idea as long as people can do horrible things to each other and the world faster than you can (or should) make them strictly illegal.
People can always think of horribly destructive ways to make money, and ensuring not just personal, but shareholder liability for them, is one of the only ways to keep things in check.
These things would happen a lot less if the ROI was not as high, and in particular, if downside risk was not minimal.
Your friendly billionaire is going to invest a lot less in arms dealers if the downside risk is not just their 1 million investment, but their entire fortune.
There are lots of good articles on this:
https://www.bus.umich.edu/KresgeLibrary/resources/abla/abld_...
https://www.occ.gov/publications-and-resources/publications/...
https://www.cambridge.org/core/journals/journal-of-instituti...
etc