1. Section 245(i)
The most important qualifications for Adjustment of Status (AOS) in the United States are: 1) legal US entry, that is, a valid stamp that is validated by the Board of Entry at the airport or border; 2) After entering the United States, you must have been a legal resident before applying for AOS. Therefore, illegal immigrants are not allowed to obtain permanent residence in the United States. However, immigration laws have exemptions that apply in these cases.
The representative clause is the Immigration and National Act (INA) Section 245 (i). To qualify for INA Section 245 (i), eligible immigrant visa petitions, such as I-140 through employment, I-130 through family invitation, I-360 or I-526 in special cases, or application for Labor Certificate (ETA 750 at that time), must have been filed with the USCIS or the U.S. Department of Labor before April 30, 2001. If you are confident that you are eligible for the benefits under INA Section 245 (i), you must submit a form Supplement A at the time of I-485 submission and submit a $1,000 penalty.
2. Section 245(k)
INA 245 (k) allows you to submit I-485 documents for AOS despite of illegal stay and illegal employment, as long as those periods are less than 180 days. INA 245(k) applies only to an employment-based immigration process though. It generously allows the records of short-term illegal stay or illicit employment to be pardoned to obtain a permanent residency. To be eligible for 245 (k), you must have legally entered the United States (i.e., not smuggled) and have had stayed in the United States at the time you filed I-485 documents. An illegal stay of less than 180 days for which 245 (k) is applicable is the period from the expiration date of the I-94 to the date of receipt of the I-485. In the case of illegal employment, it must be less than 180 days from the beginning date of illegal employment to the end of that employment.
3. I-601 Provisional Waiver
If INA Section 245 (i) described above does not apply, there is another way to apply for a waiver of re-entry period (I-601A: Provisional Unlawful Presence Waiver of Inadmissibility). After receiving the approval of the I-130 or I-140 from the USCIS in the United States, the I-601A waiver can be filed based on the approvals. If the 601A waiver is approved, and after receiving a provisional waiver, the applicant can return his/ her home country with a legitimate status to have an interview in US Embassy. If the interview goes well, the applicant can come back to the U.S. with the 601A waiver.
The most important condition of the I-601A waiver is that the applicant must demonstrate that his or her spouse or parent living in the United States will suffer extreme harshness if the applicant fails to re-enter the United States.
From the end of August 2016, the I-601A has been expanded ('Expansion' of Provisional Unlawful Presence Waivers of Inadmissibility). The expanded I-601A waiver is also including spouses or parents of permeant residents, not only U.S. Citizen. In addition, it is not limited to family immigrantion, but applies to all immigrant visa categories.