[throwaway219450]

The F/J exhange visa is tied to a specific sponsor (ie the University) for a very specific goal. There are a lot of restrictions on what you can and can't do. If your visa sponsor has its privilege revoked then presumably you have a choice to transfer to a different institute, if one will take you, or leave the country.

There is a mechanism for that transfer built into the visa, which could be used for example if your professor moved institutions and wanted to re-hire you to fulfil the original goals of your exchange program.

It's unclear if this affects all foreign academic staff, many of whom who would be on the J, or just the F visa.

Edit: apparently all exhange visas.