What consequences does one face, when F-1 is applying for AOS if they worked illegally?

Working without authorization on F1 visa constitutes a violation of status, with brutal consequences: the status is considered revoked and visa - cancelled from the first date of the illicit employment. Having a U.S. parent might, in theory, be helpful but only in some rather unlikely circumstances. Generally, there is a wait time of no less than 6.5 years from the date of filing an immigrant petition by a U.S. parent before the beneficiary can file for adjustment of status (this wait period is longer if the beneficiary is a national of Mexico (11 years) or the Philippines (21 years)). You mentioned that your friend was contacted by the National Visa Center; it might mean that your friend's parents filed a petition for him years ago. If is so, he should speak with an immigration attorney ASAP. To adjust status in the U.S., he needs to be in valid status (which he appears to have lost by working without authorization). If adjustment of status does not look likely to succeed, he can ask the NVC to transfer the case to consular processing, leave the U.S., and wait for am interview at the U.S. Embassy in his native country. The problem is that, if he stays in the U.S. more than 180 days after losing his status, he becomes inadmissible for 3 years. You said he worked for 110 days without authorization; so the time to avoid the 3-year bar is running out (if not yet gone). The bottom line: your friend has a problem; he also has some options; what he does not have is time to go trailing through immigration advice websites - he needs a very concrete, professional recommendation based on all the particulars of his case.