Legal Question in Business Law in California

Generally not. Generally the corporation is its own legal person with its own debts and liabilities that only it owes. Under certain circumstances, however, usually through failure to follow the laws and regulations of proper corporate governance, directors may have personal liability. Not surprisingly, that is more common in small corporations that lack personnel with adequate formal business training or resources to hire professional management and legal services to make sure they follow the rules, or, occasionally, in big corporations where someone's a crook. Also, if a director personally and directly does something legally wrong, the liability is theirs in the first place, even if the corporation may be secondarily liable. But most corporations that are properly managed and run provide a barrier between the corporation's liabilities and the directors, except for the direct wrongful acts of a director individually (such as sexually harassing a staff person, for example).

I agree; the term often used for finding a corporate officer or director personally liable for business debts is "piercing the corporate veil."