Without commenting on the relatively strange situation itself, it is still useful to actually read what was actually said than what was described in a letter from a third person, even if the relayed information is technically true.
The supposed basis for the claim of a zero salary is from an email allegedly sent by the department head (appendix 15):
In short, you are not teaching in 2022/2023 and you have not submitted the required outline of
your research or other engagement. I am very sorry that we cannot establish that you will be
doing any work expected of a faculty member. Thus we cannot pay you. Starting with the Fall
semester, your pay will be reduced to zero and you will be placed on unpaid personal leave.
Essentially, the professor is being put on an unpaid leave because allegedly he is not doing any work. Consequently, minimum wage laws are not engaged even if the professor is not exempt as teachers since he is not being required to do any work.
In the U.S., employers generally can do this (unless a work contract provides otherwise); in many circumstances, it is called being laid off (though the term has attracted a permanent connotation in parts of North America) or being suspended.
An indefinite unpaid leave can be considered constructive dismissal if the employer does not reasonably allow the employee to return to work. It may not be constructive dismissal if the unpaid leave is prescribed by binding employer policies or because the employee refuses to work (and the employer allows the employment relationship to continue). Even if it is constructive dismissal, it is not automatically wrongful.