The ICE Student Exchange and Visitor Program has published an updated FAQ clarifying certain issues of concern for Autumn 2020. The FAQ explains that F and M students, and schools certified by SEVP, should continue to abide by the guidance published in March. The document has additional information for DSOs.
Summary:
ICE has clarified that international students who were enrolled in a US institution as of March 9th, 2020, may be issued an I-20 and retain their non-immigrant status even if their classes are entirely online. These students may remain in the US if they are already here. If they have subsequently left the country, they are likely eligible to return to the US on their existing student visa. Travel may be subject to COVID-19 travel restrictions. Visa eligibility for travel to the US is determined by the Department of State, not ICE.
However, initial students, who were not enrolled in a US institution as of March 9th, 2020, may not be issued an I-20 if their classes are entirely online. Thus, they cannot obtain an F-1 Visa for travel to the US if they are taking entirely online classes.