Everyone should know that special options are available to aliens who have been the victims of spousal abuse by their U.S. citizen or Lawful Permanent Resident spouse. We will not discuss those cases here, but instead focus on the usual situation where there is no abuse.
If you haven't yet received your permanent resident card, the application will be denied. This can be especially problematic if you are already out of status by that time or missed deadlines for other forms of immigration relief.
If you have obtained your conditional 2-year green card, you have to file a Form I-751 to remove those conditions and make your residency permanent. Normally, this is filed by both spouses jointly. However, it is possible to seek a waiver of this requirement if you are separated or divorced, This is a complicated process requiring detailed proof of your circumstances and should not be attempted without the help of a qualified, licensed attorney.
If your green card is "permanent," meaning that it requires renewal in 10 years, the breakup of your marriage ordinarily will not affect your residency. However, you will have to wait 5 years instead of 3 years from the date of acquiring residency before you can apply for citizenship.
It is also worth mentioning that a marriage which fails very soon after receipt of the permanent residence card, when considered together with other factors, can give rise to the suspicion that the marriage was only entered into for the purpose of the immigration benefit. A conclusive finding of marriage fraud has severe penalties for both parties involved.