A sole proprietorship is simply a term for a business conducted by a single person that is not organized into a corporation or other entity. If someone starts a business without organizing an entity, he or she will be operating as a sole proprietorship by default.
The primary advantage of the sole proprietorship is convenience; there are no organizational steps to follow. The primary disadvantage of a sole proprietorship is that the owner will not enjoy the protection of limited liability available to owners of corporations and limited liability companies. In most cases, this disadvantage is so significant that people who conduct business will organize a limited liability entity rather than a sole proprietorship.
If another person becomes an owner of the business, it is no longer a sole proprietorship by definition. Assuming the existing owner and new owner do not organize a corporation or other legal entity, the new owner will transform the sole proprietorship into a general partnership.
The sole proprietorship is taxed on the owner's personal tax return on Schedule C. In other words, the proprietorship does not file a tax return of its own.