I believe "immediate relative" is eligible to AOS even though they are overstaying. The definition of immediate relative is, according to Title 8, those who does not come under numerical limitation.
Parents are immediate relative, so you know the answer.
Sec 245.1 (b)(10).
(b) Restricted aliens. The following categories of aliens are ineligible to apply for adjustment of status to that of a lawful permanent resident alien under section 245 of the Act, unless the alien establishes eligibility under the provisions of section 245(i) of the Act and Sec. 245.10, is not included in the categories of aliens prohibited from applying for adjustment of status listed in Sec. 245.1(c), is eligible to receive an immigrant visa, and has an immigrant visa immediately available at the time of filing the application for adjustment of status: (Revised 10/1/94; 59 FR 51091)
(10) Any alien who was ever employed in the United States without the authorization of the Service or who has otherwise at any time violated the terms of his or her admission to the United States as a nonimmigrant, except an alien who is an immediate relative as defined in section 201(b) of the Act or a special immigrant as defined in section 101(a)(27)(H), (I), (J), or (K) of the Act. For purposes of this paragraph, an alien who meets the requirements of § 274a.12(c)(9) of this chapter shall not be deemed to have engaged in unauthorized employment during the pendency of his or her adjustment application. (Added 7/23/97; 62 FR 39417)
And 201(b) defines immediate relatives as,
(b) Aliens Not Subject to Direct Numerical Limitations. - Aliens described in this subsection, who are not subject to the worldwide levels or numerical limitations of subsection (a), are as follows: