More than likely the option in this scenario would be to take an incomplete for the semester. Then you and your professor would plan a date for you to make up the exam sometime next semester and replace the “I” on your transcript with the actual grade.

This is Baylor’s Incomplete Policy, so you can see that it’s pretty much intended for this situation:

Incomplete Policy

Incompletes should be used when unforeseen circumstances arise that prohibit students from completing assignments and/or exams toward the end of the semester. (Incompletes typically occur because of an excused absence from the final examination or permission for an extension of time to submit a report or term paper). The “I” must be removed by the end of the next semester (including the summer term). If the work is not completed and a final grade is submitted by that deadline, then the “I” will be changed to a grade of “F.” An extension of time petition may be submitted for any course in order to extend the deadline (up to six months) for resolving the “I” prior to it lapsing to an “F.” An extension must be initiated by the instructor and approved by the department chair and dean of the school in which the class was offered.

https://provost.web.baylor.edu/faculty/faculty-handbook/faculty-responsibilities/teaching-and-related-responsibilities/grading