What type of liability implies that the owner is fully responsible for all losses and debts of the business?

Unlimited liability means that the owner is personally responsible for all of the business's debts and losses. This type of liability implies that if the business incurs debts that it cannot pay, creditors can pursue the owner's personal assets to settle those debts. This is common in sole proprietorships and partnerships, where there is no legal distinction between the business entity and the owner(s).

In contrast, limited liability protects personal assets by ensuring that the owner's financial responsibility is capped at the amount they have invested in the business. Shared liability and corporate liability do not convey the same level of personal risk associated with the debts of the business. Therefore, unlimited liability is the correct term that encapsulates the essence of total personal accountability for business obligations.