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The short answer is, while they probably won’t get in any trouble for applying as long as they don’t lie on the forms, they normally won’t qualify. Unemployment insurance is just that: insurance. It isn’t a public benefit that would cause any kind of problem with the “public charge” ground for inadmissibility. Employees and their prior employers have, in fact, paid for the insurance through payroll deductions and taxes. Therefore, a non-immigrant visa holder won’t get in any trouble – right now OR later, in connection with a green card/permanent residence petition – for accepting unemployment insurance. However, in order to qualify for Unemployment Insurance, a person generally needs to be available to accept employment. Employment-based work visas tend to be employer-specific, and require a petition by a new employer to obtain valid status for the individual. So, having been on a work visa for the employer who terminated or laid off the foreign national generally means that the person IS NOT available to accept new employment, and so not eligible for unemployment insurance.