It is not clear what you mean here by "non-resident." If you were legally working in California and have been let go from your job for anything other than some form of gross misconduct, you are eligible to apply for and collect UI benefits regardless of your residency status. If by non-resident you mean that you were working somewhere other than California, then you are not eligible for California UI benefits and would have to apply for those benefits in the state where you had been working.
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Do you mean non-citizen or non-resident? Non-residents are not authorized to work in the U.S., and therefore are not eligible. To collect UI benefits, non-citizen applicants must establish that they were in satisfactory immigration status and authorized to work in the United States, when earning the wages used to establish their claim.
In addition, the non-citizen applicants must provide proof that they remain in satisfactory immigration status and are authorized to work each week that benefits are claimed. Non-citizen applicants will be required to provide specific information from their employment authorization documents issued to them by the United States Citizenship and Immigration Services (USCIS). In some cases, non-citizen applicants will be asked to provide legible copies of their employment authorization documents. EDD verifies immigration status and work authorization through an electronic system maintained by the Department of Homeland Security.