I think you may have asked the wrong question.
Various parts of the case expand, and some of them compress again once pressure decays. If that weren't the case (no pun intended), you wouldn't be able to extract the case.
If the issue, however, is incipient case failure in the case (there we go again) of bottleneck rifle cases, the issue is stretch, not expansion.
What happens is this:
You chamber the case in a chamber that is larger than the case (else the bolt wouldn't close).
When the firing pin strikes the primer, it pushes the case forward. The greater the headspace, the further forward it goes.
As the powder combusts, gas pressure causes the neck of the case to expand against the walls of the neck area of the chamber, causing a gas seal.
As the bullet now begins to move, pressure tends to push the head and web of the case aft, into the breech face. Since the neck is still fixed in the forward end of the chamber, this force tends to stretch the case in the area just above the web.
Repeated firing, sizing, and firing again causes repeated stretching, with each cycle thinning the walls of the case just above the web. If the process is unchecked, the case will fail at that point. (Before this happens, you should see a ring, brighter in color than the rest of the brass) just above the web.)