Well partly...not just oxygen gets depleted. A bunch of nasties also get created in the fire suppression process. Sulfuric acid gas, HCl... how do I know... well kids pull up a pool noodle for a good story...
I was a part of a NASA group in my early mad scientist days that studied heat transfer and fire behavior related stuff. The group I was a part of did the theoretical heat transfer calcs and computer simulations to define the boundaries of the actual experiments. The science was thick and mind numbing but the experiments were cool because we got to blow things up and set things on fire. We were a group of rowdy physicists stuck a building with bunch of stodgy chemists (with all due deference to Joyful) called the "Chemical Research Project Office" or more fondly known as "Crud-O"!
One of the studies we took over from the Army. They wanted to find out what happens when an armor piercing heat round hit the gas tank of a Tank or Armored Personal Carrier (APC) and the Halon fire suppression system puts the fire out. The Army's version of the study stuck a bunch of pigs (because they have an anatomy similar to humans) in an APC and they shot at it with a heat round. The conclusion of the study was ..."The pigs died". That's it. There was no analysis of the resulting atmosphere, no pressure transducers to see what kind of shock wave there was, and no autopsies of the pigs to determine what they actually died of... they just did. This became the rallying cry for every bad science experiment we encountered from then on.... we would look at each other and just say... "The pigs died".
So our version of the experiment we did on the computer first.. this was pre PC's, Big IRON IBM main frame stuff. We wheeled boxes of computer cards over to the computing center to load up our app and our data set... the numbers it spit out were scary.. H2SO4 in toxic levels.. nah, can't be. Must be a bad decimal place... so we ran it again. and the same stuff came back. So we told the guys at White Sands that were building the test APC in the dessert to configure their samplers for H2SO4 and HCl gas in these "ranges"... they poo-pooed us but did it anyway. And sure enough when they shot the test APC, they found those chemical in the concentrations we predicted... virtual stoichiometry was the hero of the day. Then we passed the information on to the rest of the fire industry from there.... Our conclusion? The shock wave of the blast probably killed the pigs first, and the atmosphere that resulted from the Halon putting out the fire finished off the rest of them... but in our version of the experiment.. no pigs died.