A person traveling on advance parole may still return to the US without triggering the unlawful presence bars. Citing Matter of Arrabally, the Eleventh Circuit held that the petitioner was not inadmissible under §212(a)(9)(B)(i)(II), because she left the United States pursuant to a grant of advance parole.
Advance Parole document filed on form I-131 can save an immigrant a lot of troubles. Under the INA (Immigration and Naturalization Act) a person accumulated unlawful presence in the US, would be inadmissible for 3 or 10 years if the person departs the US before he/she becomes a US permanent resident.
However, recent cases confirmed that travel after a grant of advance parole does not constitute “departure” for the unlawful presence bars purposes. You can read the 11th Cir. case HERE.