I'm sorry but there's almost nothing that can be done while they remain in the US. To get a green card while remaining in the US (this is called "adjustment of status") requires that one be in a legal immigration status. There is an exception by marriage to a US citizen, but only where the intending immigrant has legally entered the US and simply overstayed their non-immigrant visa. The only other option, which I hope does not apply in your case (you'll see why) is the Violence Against Women Act (which applies to men, too). VAWA permits the victims of domestic violence and other "extreme cruelty" at the hands of their abusive US citizen or green card holding spouses to adjust status even if they entered the country illegally. The other way people in this situation adjust status is through an older provision of US immigration law called "245(i)", but this won't help in your situation because it requires the intending immigrant to have been in the US on December 21, 2000.

They will have to leave the US in order to have any hope of returning legally. The problem with doing this is that after accruing 1 year or more of "unlawful presence" (i.e., being illegal) in the US will trigger, upon leaving the US, the "10 year bar" on re-entry. That is, if they leave the US, they won't be permitted to return for 10 years. You can apply for a waiver of this 10 year bar, but such waivers are highly discretionary on the part of the US consular officers who deal with them, and to qualify you must show "extreme hardship" to a US citizen if they're not permitted to return. This is very difficult to do and not something to count on.

So they're stuck, really. Under current immigration law, they can't adjust status while remaining in the US, and if they leave, they likely won't be permitted to return for 10 years. There are over 12 million people in a similar situation in the US right now. Everyone agrees that something must be done to provide some path toward legalization, but it's not clear when that will happen or who will benefit. Most people in this situation decide to stay in the US and hope immigration laws change in the future. Something will change, if not this year then next, but it's impossible to predict how it will change. I'm sorry that's the way the law is right now, but it is. Good luck with everything and I sincerely XXXXX XXXXX immigration reform does take hold that it helps your situation.