The short answer is "Yes", but they may need a waiver for hte overstay. I would suggest that you contact an experienced immigration attorney for a face-to-face consultation and give him/her all of the facts surrounding your parent's situation. (S)he would then be in a better position to analyze their problem, advise you of your options and, if possible, make sure that the necessary paperwork and documentation is properly presented so as not to delay the process. Good luck.
In connection with an adjustment of status application process in the Immediate Relative visa category (such as an adult U.S. citizen petitioning for a parent who entered the U.S. lawfully and with inspection), the fact that the parent may have overstayed an initial visa will not stand in the way of eligibility. It would be wise for you and your parent to consult with an immigration attorney, who, after learning all of the relevant information about your family, could advise about eligibilities, options and strategies, and could offer legal representation in the often complex application process.
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