Unlimited liability in business implies that the

Liability in business refers to how far an owner can be made to pay the debts of the business. Under unlimited liability, the law does not draw a line between the owner's personal wealth and the business's wealth, so if the business cannot pay what it owes, creditors can pursue the owner's personal belongings, savings, and other property to recover the debt.

This is why the situation is described as the owner's private property being usable to settle business debts: the owner's risk is not capped at whatever was invested in the business, it extends to everything the owner personally owns.

Saying the risk is limited only to the amount invested describes the opposite idea, limited liability, which protects shareholders of companies. The idea that property should not be used to secure loans is unrelated to liability for debts, and paying debts with subventions describes how some public enterprises are funded, not how liability works for sole traders or partnerships.

A quick way to remember this: sole proprietors and ordinary partners have unlimited liability, so their personal assets are always at risk if the business fails; only shareholders in limited companies enjoy the protection of limited liability.