(a) That's right. A company is liable to pay its debts from its assets. What happens if the assets are insufficient? Logic dictates that the shareholders, as the ultimate owners of the company, are liable to contribute as required and this is historically what was required. But unlimited liability of this kind is a great risk to shareholders. Except in the case of small companies, where a few individuals have multiple roles as members and directors, the members of a company do not participate in the day-to-day management of the company, and it is hard for them to evaluate, control or foresee the risks. Unlimited liability for an insolvent company's debts is therefore a great disincentive to becoming a member of a company.
There is more than one way of deciding the extent of liability of members of a company for the company's debts. It is on this basis that companies are distinguished as unlimited companies, no liability companies, companies limited by guarantee or companies limited by shares. Companies limited by shares are the type of company commonly used for operating a business.
In relation to companies limited by shares, the concept of limited liability is that shareholders in a company are only held legally liable for the unpaid debts of the company to the extent that they have agreed to purchase shares in the company. Suppose that a shareholder has agreed to purchase 1000 shares for $100 each. They might pay the agreed amount up front, or they may agree to pay it from time to time as the company requires. Either way, the liability of that shareholder is limited to the amount paid or promised for the shares taken. This limitation on a shareholder's liability allows the investor to limit their risks. It also allows third parties to establish what the limit of the company's share capital is.
Of course, it is possible for a company to raise very little capital by means of issuing shares. In a small company, for example, a proprietary company operating a one-person business, with a single shareholder/director, there may be no financial need in such cases to issue more than a single share, for a nominal amount. This means that the single member is carrying no financial risk at all. The company will acquire its capital elsewhere, eg by means of loans. In such cases, the creditors are completely financing the company and their risks are greater.