She entered US with Mexican Passport and was given a social security card based on her passport, but no green card.
She could be eligible for work without having a green card. Consult the guidelines in form I-9 (Employment Verification Eligibility). You can find it on www.uscis.gov, under Forms tab. There are a host of documents that could make a person eligible to work and they are listed in I-9 form.
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