QUESTION

Our employee went out on FMLA leave and has stopped all communication with the company. What now?

SHORT ANSWER
You should respect the need for leave and the fact that your employee is not at work, but periodic and regular check-ins can be expected. 
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FMLA leave is not a vacation. You should respect the need for leave and the fact that your employee is not at work, but periodic and regular check-ins can be expected.  If an employee fails repeatedly to respond to respectful inquiries, there is some possibility of job abandonment.  However, given that the employee is on leave, termination must be carefully approached.  It is worth taking the time to document consistent failed efforts to reach the employee.