If my employee is out of paid time off, do I have to give her unpaid time off for an important annual summer gathering?

No, not unless you have a policy or practice, or you have entered into some sort of agreement that entitles her to take this time off. Employees often exhaust their paid time off, whether because of poor time management or some sort of unplanned need for time off. Even if it is an important event, like a wedding or funeral or family gathering, companies are generally empowered to set the terms and conditions for employees' work schedules, including leaves of absence. There are always exceptions based on the circumstances of the employer, employee and situation for matters such as (for example) military duty, the birth of a child and medical necessity, but outside these exceptions employees do not have an entitlement to pick and choose their schedules and days off, unless given to them by the company.

 
 
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