While extreme cases are the easiest to imagine, in real life the plaintiff almost always argues to pierce the veil and the defendant always argues the opposite, and both sides earnestly believe that they are right.
It's so exceptional in the UK you can run a series of fraudulent businesses which are incorporated, "buy" services, don't pay for them, then declare themselves insolvent, rinse and repeat, and there's a fair chance you'll get away with it.
It's called phoenixing. There are good few bans for it every year, but almost no convictions for fraud.
Not in the US it’s not. LLCs don’t shield your assets from personal negligence. So if you have a single member LLC with no employees (very common), an awful lot of what prompt a successful suit will be because of negligence on your part.