individuals who entered the U.S. without inspection cannot adjust their status to become a lawful permanent resident (get a green card) based on a U.S. citizen child's petition, unless they qualify for a specific exception like INA 245(i) or a waiver of inadmissibility

Even with a U.S. citizen child, they would typically need to depart the U.S. to attend an immigrant visa interview at a U.S. embassy or consulate abroad. 

If your U.S. citizen child is 21 years old or older, they can petition for you as an immediate relative by filing Form I-130.

Yes, in some cases, parents of U.S. citizens may qualify for relief like Parole in Place or other waivers. Consult an immigration attorney for personalized advice.