Suppose there is a fire inside a large spacecraft, and there are crewmembers trapped inside. Is it possible to extinguish the fire by venting and then repressurizing the cabin, without killing the people?
Depressurization causes little if any harm so long as it's neither too fast (if the air in your lungs exits too fast it will do severe damage), nor too long (due to a lack of oxygen.) So long as the space involved isn't too big these requirements can be met.
However, if it's a solid material that is burning (and how many flammable liquids or gases would be on a space station anyway?) you would be facing the definite possibility that the fire would simply reignite when you put the air back in the room. In vacuum there would be little cooling of the hot materials, they very well might remain above ignition temperature.
Scientific American author Anna Goslin reported 2008 on NASA experiences with depressurization in animal tests and also in accidents involving humans. According to this article , surviving a near-vacuum for a short time is possible.
I doubt however that this would be a viable approach to extinguish an onboard fire. You would need to vent quickly, then repressurize with nitrogen or any other non-oxidizing gas that may be available. The crew would need to use oxygen masks like in aircraft. Venting and repressurizing a compartment of reasonable size within 60 seconds might be too challanging.
EDIT after additional thinking: Oxygen masks would probably not prevent the crew from going unconscious, as the gas-exchange in their lungs will not work at all at low ambient pressure. The emergency venting valves would need to be designed to not create too much thrust. You must prevent that they suck in any objects and get stuck. The chilling effect of adiabatic expansion of the inert gas would be enormous.
2nd EDIT: Read this Aviation Week article to get an impression of gas exchange problems under low pressure conditions.