Immigration takes the position that unpaid internships are employment, therefore it is not permitted. The one exception is if you are doing true volunteer work such as changing bedpans at a hospital or serving food at a soup kitchen.
If you are in the US without permission or your status is expired, i would not advise working at all, paid or unpaid
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Technically illegal immigrants can't do any internships--paid or not--because they are not allowed to be in the country.
Moreover, any position involving employment verification (which often takes place even for unpaid positions, especially at larger companies) carries some risk of discovery and, potentially, deportation.
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I agree with both of my colleagues.
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