How does the plane of focus change when you focus on distant objects?

If I have a 100mm f2 lens and focus on a person 5ft away at f2, say the plane of focus is 5cm thick. So everything from the subject's nose and 5cm backward is in focus.

If the person is now 50ft away and I focus on them, is the plane of focus still 5cm thick? Or does the plane of focus get deeper the further your focused subject is?