Probably. When and employer terminates you for giving an advance notice of resignation you are nearly always eligible for unemployment benefits unless you are disqualified for misconduct. Normally an employee who voluntarily quits is ineligible. However, when the employer unilaterally terms you prior to the date of your advance notice termination, you become eligible. You can always call the unemployment department or contact a local employment lawyer for state specific law governing your firing.
Best of luck!
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Likely, yes. Generally when you choose to leave your job, you are not eligible for unemployment. However, when termination occurs prior your leave date you generally remain eligible for benefits due to your early termination. You can contact TWC for details, but if you have any issues get with a local attorney immediately.