Our company requires employee to utilize vacation and sick time while on FMLA. Once they have exhausted that time it becomes unpaid. Do you think that they employee should then be allowed to take that vacation time at a later date if it is unpaid?

What we think is irrelevant. It's completely up to the company. If they don't want to let the employee take unpaid time off at a later date, they are perfectly within their legal rights not to allow it.