Not quite. In the US this condition is handled at the back end. Running a corporation or LLC without sufficient capitalization can be grounds for piercing the liability shield in a lawsuit.
I have the impression the situations where that actually happens are at least arguably serious misconduct, and usually targeted at someone with significant assets.
A construction company that pockets ten million dollars and doesn't build anything probably can't shield its owner this way, but a single-developer software consultancy that pockets ten thousand dollars and delivers buggy code can.
Haven't heard anything about LLC capitalization in this context. Liability shield can be pierced, but only if LLC is misused (i.e. "when the company is treated as a personal "alter ego" and used to commit fraud, injustice, or illegal acts"). Lack of capitalization is not one of the reasons as long as you treat it as a company, not your wallet.
Have to prove fraud to get there. "Under" capitalization is a judgment call. Effectively, it's very rare. An LLC launches with effectively zero dollars literally dozens of times a day.
This is a core difference between common law and civil law. In common law systems, things tend to get sorted out after the fact, with a judge's discretion, only if things go really wrong. In civil law systems they try to design a perfect system of laws that makes problems impossible.
> Running a corporation or LLC without sufficient capitalization can be grounds for piercing the liability shield in a lawsuit.
Which is exactly how it should be handled, IMO: Deal with the abuse situations directly.
Forcing new companies to capitalize with an arbitrary amount of money at time of founding penalizes small players who want to start a company. It's also not a hurdle at all for large players who want to commit large frauds.