My understanding is that under certain circumstances, such as marrying a US citizen, the USCIS can ignore any past violations of immigration law.[1]
"If you are a foreign citizen who is in the United States without permission, having overstayed your visa, you can indeed cure the problem if you enter into a bona fide (real) marriage with a U.S. citizen and then apply for adjustment of status (a green card)."
You are correct that for most visas and green cards, any violation of immigration law means that your application will be denied.
Interesting. There was an episode on This American Life a few years ago about a Mexican-American couple. He had been in the US illegally and he had to leave and wait for ten years before he could come back legally even though they had married in the US. So they moved to Ciudad Juarez. He's working at a local factory, she's commuting to El Paso every day. IIRC they weren't entirely happy with their situation but they didn't complain either.
"If you are a foreign citizen who is in the United States without permission, having overstayed your visa, you can indeed cure the problem if you enter into a bona fide (real) marriage with a U.S. citizen and then apply for adjustment of status (a green card)."
You are correct that for most visas and green cards, any violation of immigration law means that your application will be denied.
[1]http://www.alllaw.com/articles/nolo/us-immigration/visa-over...