Legal Question in Immigration Law in Massachusetts

If a non-resident marries a USA citizen, and a non-resident came to USA legally (on a visa), then yes, he can apply for a Green Card (permanent residency) and obtain a SSN.

If a non-resident marries a permanent resident (not a US citizen, but a Green Card holder), the situation is different. If a non-resident is in the country illegally and came illegally, he will not be aligible to apply for a Green Card and a SSN. He might be able to do so when a spouse becomes a US citizen.

It's not clear from your post what is this non-resident's status in USA, and how they came to USA (on what visa and when).

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