system
Given the following post, respond as if you're commenting on Reddit:
human
Does a binary star system create a dynamic Goldilocks zone?

Would 2 or more stars in a system create a habitable zone which is always changing in position in respect to the stars’ location?
gpt
If you mean an elliptic zone whose boundaries (min and max distance from the center of mass of the system) fluctuate, then yes.  We'd only call the portion that is stable a 'goldilocks zone', though. 

If you mean a zone of physical parameters that allow habitability and actually orbits around and among the components, or (quasi-)periodically 'appears' from place to place, then that too is possible in principle, but the system probably (~certainly) wouldn't support a planetary orbit that follows such a zone. 

'Habitable/goldilocks zone' implies stability over periods where life can spring up and evolve.  From the only example we have, this means millions to billions of years.  For your wording of "zone always changing in position", I'd therefore say:  No.  Goldilocks zones are stable (by definition).