They should be able to apply for asylum the way the International law legally allows them to.
“The United Nations 1951 Convention Relating to the Status of Refugees and the 1967 Protocol Relating to the Status of Refugees guides national legislation concerning political asylum that the USA signed.
AND our own FEDERAL LAW:
The United States Refugee Act of 1980 (Public Law 96-212) is an amendment to the earlier Immigration and Nationality Act and the Migration and Refugee Assistance Act, and was created to provide a permanent and systematic procedure for the admission to the United States of refugees of special humanitarian concern to the U.S., and to provide comprehensive and uniform provisions for the effective resettlement and absorption of those refugees who are admitted.
That’s the LAW. We are a nation of LAWS. PERIOD.