Can an employer put an employee on an unpaid leave of absence?  It is an
international company with offices in the US and other countries.  The
state this question applies to is in Tennessee.  The employer tells
the employee they will go home, not work, and be paid for unused
vacation time then they will be put on an unpaid leave of absence.

Sounds like a "temporary layoff".  This person likely qualifies for
unemployment comp.  The person should also feel no loyalty and should
search for another job.