A holder of the TPS status is allowed to apply for advance parole: a document authorizing the alien to travel abroad and return to the United States.
Section 212(d)(5) of the Immigration and Nationality Act (“INA”) grants the Attorney General authority to parole into the United States aliens seeking admission “on a case-by-case basis for urgent humanitarian reasons or significant public benefit.” 8 CFR ยง 212.5(f) authorizes USCIS to grant advance parole to aliens who will travel without a visa, by issuing “an appropriate document authorizing travel.”
The significance of the parole is that if a person entered without inspection, received a TPS or DACA status, traveled on parole and was in fact paroled back to the US, the person is no longer an EWI, and, can adjust status to one of the permanent resident.