For those that don't hand load, it is a well documented procedure for making cases for obscure cartridges. For example the 303Epps is made by firing a 303BR in an Epps chamber. The procedure as H4831 mentioned earlier is known as fire forming.
This is when it is done on purpose, with knowledge of what you are doing, and the correct cartridges to do the fire forming, there is little danger.
Every firearms owner should know the hazards associated with firing incorrect rounds in your rifle. It can be disastrous for your firearm, and could result in your premature demise. If you don't know, don't do it!
Showing folks how a 20ga shot shell will lodge in the bore of a 12 is standard safety course stuff. But other things can happen. Bullets can lodge in the barrel, head space can cause violent case separation. Bits of the case can break off and lodge in the barrel. The center can blowout of a bullet, leaving the rest in the chamber, neck, or bore. Pressures can just be too much resulting in Kabbom, Lots of things, boom on your next shot, or even your first. Be careful, and be knowledgeable.