While it is true that independent contracts are ineligible for UI, many employees are incorrectly labeled independent contractors by their employers. An independent contractor is someone who is in business for him or herself. Many companies label short-term employees as contractors in order to avoid certain obligations to employees (including UI benefits).
If your employer controls how you perform your work and controls your schedule, you may really be an employee and therefore eligible for UI benefits. You must notify the state because they will likely not have record of your employment and therefore may find you ineligible for UI benefits. Your state labor department may have additional information on how to determine whether you are an independent contractor. For more information, see our site's independent contractor page.