Wiktionary
n. (context legal English) A business that is wholly owned by a single person, who has unlimited liability.
Wikipedia
A sole proprietorship, also known as the sole trader or simply a proprietorship, is a type of business entity that is owned and run by one natural person and in which there is no legal distinction between the owner and the business. The owner is in direct control of all elements and is legally accountable for the finances of such business and this may include debts, loans, loss etc.
The owner receives all profits (subject to taxation specific to the business) and has unlimited responsibility for all losses and debts. Every asset of the business is owned by the proprietor and all debts of the business are the proprietor's. It is a "sole" proprietorship in contrast with partnerships (which have at least two owners).
A sole proprietor may use a trade name or business name other than his, her, or its legal name. They will have to legally trademark their business name, the process being different depending upon country of residence.
Usage examples of "sole proprietorship".
Converting the House of the Sleeping Dragon from its rare status as a sole proprietorship to a more conventional clan corporation had not been quick or easy.
The captains' jealous hoarding of information was inadvertently giving him sole proprietorship of the job of fleet coordinator.
There was evidently a little the best chance of light, air, and sole proprietorship on the pole.