Ahhh so this is different from camera movements [1] used in large format photography to manipulate the focal plane and achieve various effects. These movements take place only before the exposure, not during.

[1] https://en.wikipedia.org/wiki/View_camera#Movements

Fairly common, also.

Consider panning, in sports photography, where you track a player in a field while the background blurs from side to side. Also in motor sports, some nature photography, or any time a photographer wants a motion effect, perhaps in street photography, or even snapshots at family events.

Edit: similar effect in travel photos, where someone shoots from a moving vehicle - far background might look fairly stable, near background (cyclists & vehicles) blur, people in your vehicle might be stable, depending on shutter speed and how much bouncing on the road.

One pretty easy (I didn't know the name at that time) example is, a still person in front of a moving train (at station for example). E.g. https://www.instagram.com/p/BPpyrCMhwN_/?igshid=NmE0MzVhZDY=

Though this is moving background, not moving camera.