It is important to handle any employee request for leave, or related in any way to family or medical issues, properly. In the case of PFML, it is not the employer but the state that determines eligibility.
As an employer, however, you are obligated to inform the employee about the availability of leave under state law and provide information about how to apply.
You should also have an honest and respectful conversation about what kind of leave the employee needs. They may, for example, only need or want intermittent leave- certain days off during the week, or reduced hours during the day. This may help you in planning for coverage during the leave, and help them stay connected to the workplace in the interim.
It is also never to early to start thinking about their re-entry after a leave. You are required to hold either their job or a comparable job open for them during the allowed periods of leave. You are also not allowed to terminate them on their return if it is because they took leave. For this reason, if there were performance issues or other problems that existed before the leave, you should make sure those are documented, and when the employee returns make sure expectations are clearly communicated.
Learn more here about the Massachusetts Paid Family Leave Law.