If you're in the country legally, why wouldn't you get a social security number, and what would make you think you're "no considered a 'real person' in this country"?
Since I don't have a social security, then I'm not real in this country, there's no register of my existence here, I'm just under a type of work visa, so, it's like my "husband" had gotten married to a fictional person, once there's no way to proof that I'm a real person here. My name? My passport number? Lol. That can be any person. I'm 100% our "marriage" is not real, has no legal value, since I'm none in USA.
Wrong. Why would you think that?
If you marry someone else in the U.S. without first divorcing your spouse, you would be guilty of the crime of bigamy. Whether doing the same thing in some other country would be bigamy under that country's laws obviously depends on what other country we're talking about. What makes you think you're "nothing in this country"?