I have forgotten more about immi law than you will ever know.
Universities typically hire foreign students enrolled in US universities for cap-exempt H1s for research or academic positions, by filing a petition with USCIS. Those petitions can still be filed and most of the students are in the US anyways.
H1B program cannot be suspended by EO. Only entry of people to country can be.
I wish more people UNDERSTOOD immigration law. If they did, they would know how toothless this really is. Some common misconceptions:
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H1Bs are issued annually in April. All the work permits for this year have been issued, and most people of 2020 batch are already in the country. Next issuance does not come till April 2021. Which cannot be suspended without congress.
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You do not need a visa to remain in the country legally. Visa is a permission to enter. I-94 is permission to stay. If you are already in the country, you can extend your I-94 without renewing the visa.
What 1 & 2 means is that the only people who are affected are those few who were unlucky enough to be outside the country for vacation or business when the borders shut down, AND had an expired visa on their passport. A very small number. They would not have been able to enter anyways because US consulates that issue visas are closed due to Covid-19 for the foreseeable future.
L1s are a slightly different story.
13C is no first class LOL