Some people in special situations may be able to obtain permanent residency because they have been in the U.S. so long and it would be inhumane to force them to leave.
Some laws make it difficult for a person who has been in the U.S. illegally to obtain legal status.
In addition, the waiting list for permanent residency is so long that a person could be required to be separated from family members. Therefore, you should see an experienced immigration attorney for more specific guidance. The immigration laws provide for permanent residency for persons who have certain designated family relationships with U.S. citizens or permanent residents. The relative must petition for the non-citizen. The relationships are very specific and the person must neatly fall within one of them.