I would say no, it's not appropriate. It's not just about whether the course is paid for, it's about the use of the employee's time.
When someone is gainfully employed, and the status quo is that they will continue to be, the company allows that employee to use otherwise productive work time to get the training because there is value to the company to have that employee receive the training, to make them more capable employees as they continue, into the future.
It may be an unrecoverable loss for the course fees, but there is a loss in remaining productivity for the company if that person takes away from their remaining work time to get training that will provide no value to the company, ever.
As long as they are still employed by the company, the company should get value from that remaining work time, since the employee is still being compensated for their TIME at work.
If there is enough free time in the employee's time away from work, maybe I could see getting permission to access that, but will that additional time spent taking the course, while away from work, potentially impact that employee's productivity when they are back at work? I can see an employer making that argument, as well, especially if there's a good chunk of time one spends taking the course.
