No, it doesn't. Basically, anyone can operate as an independent contractor or sole proprietorship when selling consignment items. There is not a requirement to become an LLC, that is more of a personal decision as the LLC offers certain protections from liability that the Sole Proprietorship does not have.
Whether or not you form an LLC or just sell as an individual, you will report all of your income on a Schedule C, so the formation unless you elect to be treated as a S-Corp, will not make a difference when it comes to filing your taxes.
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