I'm writing a very late answer, partly for the edification of other readers, to support the OP's situation, and to highlight the academia varies more than you think it does principle.
I'm at a large U.S. university (CUNY) that currently uses a similar menagerie of final grade codes, that record different situations for not-passing, and handle them in different ways. A non-exhaustive list includes:
- WN: Student never participated in class.
- WA: Student was administratively withdrawn for immunization non-compliance.
- WU: Student was withdrawn unofficially by virtue of stopping attendance at some point.
- W: Student officially requested to withdraw from the class.
- INC: Student had some component of work incomplete, and is expected to be able to complete it outside of class with instructor before end of next term.
- F: Student completed the course but did not succeed at passing, due to failing-level work.
In addition to this, there's also a "refund period" of about the first week where a student can drop a class, get their tuition back, and have it be entirely expunged from their record.
I think that all of the W-type grades avoid having any impact on the student's GPA. The WN grade gets reported by faculty about two weeks into the term (and has monetary impact; I think financial aid gets clawed back by state/federal agencies). The WA is assessed by administration about one month in. W's are accepted at any time up to and including the last day of class. WU's are assessed after final exams are given.
The evolution of this system has (over the nearly two decades I've been at the institution) evolved to make it more and more likely that failing grades are kept off a student's transcript. For example, when I started, to receive a "W" grade, the student needed to be currently passing the course, had to get an instructor's approval signature on a form, and could only do so up to about the halfway point in the term. At some point that faculty sign-off form went away, as well as the requirement that the student be passing the course. Then the deadline was pushed further into the term, and now one can withdraw (at will, by web portal) at any time, including on the last day of class.
Moreover, the "WU" grade was introduced so that students are presumed to have withdrawn even if they don't ask for it -- and this is broadly what the OP is dealing with. If a student simply stops attending class, they are expected to get a WU grade. If a student attends class for the entire term, submits all assignments, and just skips the final exam, then the assumption is now that they should receive a WU grade (and so avoid reducing their GPA).
So: As others have advised in the situation, someone like the OP should read their school policies carefully. In our case, we have a very formal multi-page memo that everyone consults for the decision process on which flavor of grade should be assigned. In our case, the school really, really wants instructors to be assigning WU's instead of F's, because (I presume) it boosts student GPAs, likely increases retention, and lets the school retain their current and future tuition payments.
There's a piece of fine print in our policy that says instructors may instead opt to assign an F grade if students submitted more than half the work for term and received failing grades for it; but almost no one (faculty, students, administrators) is aware of that clause, so one needs to be cautious about using it. E.g., students who are failing late in the term will likely just ghost the course, not request a W, and be surprised if they get an F instead of a WU. Previously there was a window where W's were not available, but WU's still were, and in that era I would get some students requesting the WU from me instead of an F -- exactly like the case of the OP. (Now that W's cover the whole term, cognizant students use that option instead, so I haven't received these requests in a few years.)
In summary: The school likely has a formal recommendation/decision-process for the described grade zoo. The instructor in question should find that and read it very carefully.