negative shareholder's equity: legally possible...? Corporate Law

A privately-held California corporation (C-Corp), very thin-capitalized, has had net losses for the last few years and now cumulative deficit (i.e. negative retained earnings) is about to more than offset the owner's contributed capital, which will lead the company to a situation where the comapny's total shareholder's equity is becoming negative. Is this situation allowed by corporate laws?

I would appreciate thoughts/comments from someone in the list.