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This is the exact type of situation where you would be entitled to unemployment benefits. You are out of work through no fault of your own... you didn't quit, you were not fired due to violations in the workplace. The only issue is that the company is a non-profit. There are a few exceptions for non-profits, such as religious exemptions, but the vast majority of non profits are subject to the same rules as other employers regarding unemployment. So it most likely is no problem.
You don't say what State this is, with that information, I can answer you definitively.