A person who came here without a visa has extremely limited options, even if they marry a U.S. Citizen. It is unclear whether the law will change, but it is very easy to get into trouble. If she or her parents were petitioned by April 30, 2001, then there may be hope, but more information is needed to know if paying the penalty fee will result in success.
I strongly recommend an appointment or teleconference with an experienced immigration attorney. Paying for the appointment is cheap insurance to avoid paying thousands of dollars in filing fees only to be denied and possibly referred to immigration court for deportation.
The above is general information and does not create an attorney client relationship.
The ability of your fiance to adjust status in the US will depend on several factors.
If those factors are not in her favour then her option is to leave the US and seek immigrant visa in the US consulate in her country.
Unfortunately this will subject her to a bar on re-entry and based on the length of the period of her unlawful presence in the U.S.
One of such factors is but not limited to her ability to rely and benefit from on a previously filed petition by a family member or an employer on her behalf or a previously filed petition for his parents which list her as a child on the petition.
It is not necessary for any of the petitions to have been approved, it could even have been denied, as long as it was “approvable when filed", she can rely on it. The important requirement is that it had to have been filed on or before 30 April 2001.
Another option is to investigate any TPS filing on her behalf or on her parent's applications.
You are advised to contact an immigration lawyer to discuss the case and find a way forward.
You are certainly welcome to contact me via the link provided below.