If your son's soon to be spouse last entered the U.S. with inspection but is an overstay, the good news is that she should be able to file for and obtain her green card from within the U.S. based on marriage to a U.S. citizen. It is true that while most individuals who are here as overstays and/or have worked without permission are ineligible to obtain permanent resident status from within the U.S., this is not the case if you are applying for permanent resident status based on marriage to a U.S. citizen.
Addressing the last lawful entry issue, she may still pursue permanent resident status from within the U.S. based on marriage to a U.S. citizen. This is generally known as the adjustment of status process and requires filing the I-130, I-485, I-765 (work permission), I-131, I-864 affidavit of support, I-693 medical etc.
You can find info on the green card process based on marriage to a U.S. citizen at:
Your issues with the law should not necessarily prevent you from sponsoring her for her green card based on marriage.
Considering that she is a long overstay, they may want to consider consulting with an experienced immigration attorney before filing any paperwork.
Andrew M. Wilson, Esq.
Serotte Reich Wilson, LLP