Based solely on the information presented in this question, Ms. Hughes would clearly be liable for the unpaid debt. The reason for this is the fact that Ms. Hughes owned Sweetie’s Cupcakes as a sole proprietor and signed the loan papers as such.
Sole proprietorships are a very common form of business ownership. It is very easy to set up and is therefore attractive to many people who are starting their own businesses. The problem with sole proprietorships is that they do not do a good job of shielding the owners from risk and liability. As the link below tells us,
Both the business assets and the personal assets of the sole proprietor are subject to claims of the sole proprietorship's creditors.
In a sole proprietorship, there is no distinction between the person and the business. All of the liabilities that the business incurs are the responsibility of the person who owns it. The person’s personal assets can be used to pay obligations that the business has. This is in contrast to a corporation, which is separate from the person. If Ms. Hughes had created a corporation, she would not personally have been liable for the debts. However, since she created a sole proprietorship, there is no protection for her and she must pay the debts.