Can an adult child file for a parent to stay in the U.S. if the parent is illegal and has been here for years?

I assume that the adult child would be a U.S. citizen. If the parent entered the U.S. legally with a visa and overstayed, or was paroled into the States, or if entering illegally is the beneficiary of Section 245(i), the adult child could petition for the parent and the parent would be eligible to adjust status in the U.S. A beneficiary of section 245(i) is one who is the beneficiary of a bona fide labor certification application or immigrant visa petition filed by April 30, 2001, and was physically present in the States on December 21, 2000. The physical presence requirement on December 21, 2000, is not applicable to those who can qualify under an earlier version of Section 245(i) if they had a bona fide labor certification application or immigrant visa petition filed on their behalf by January 14, 1998.