Ahh, vent free heaters. They are terrific when used properly. I have rolled out a couple I keep in storage as PG&E is going to turn off the power again soon. They are designed to be "supplemental" heat. Where you get into trouble with them is trying to use them as the sole source of heat. VF Htrs have ODS pilot assemblies. Oxygen Depletion Systems operate just a described by the OP. In a confined space without sufficient make-up air the burner consumes the oxygen in the space. Normal air is 20.9% O2. As the O2 level gets into that 18-18.5% range there isn't enough O2 to support a strong enough pilot flame, the thermocouple cools and the gas vale drops out, as designed. I used to have an ODS box I used for sales demos. The flame of an ODS pilot will just touch the very tip of the T-couple. As the O2 drops you can see the pilot flame feather off and the MV's aren't generated causing the gas valve to drop out.
Cleanliness is key on a VF htr. That is especially so on the pilot assembly. Compressed air is the tool of choice for cleaning, but be careful. My Rinnai Vent Frees I clean with 100# of air. Use 50# on almost any other ceramic burner and you will blow it away. Get a can of compressed air with the small tube to clean the pilot and blow right back down the the pilot tube. The other thing about VF is odors. Anything that is airborne in the space, dust, fumes, perfume, po-pourri (sp) is going to go through that burner and I can guarantee that it will come out smelling worse than when it went in. Try painting around one
The State of CA in its infinite wisdom is the only state in which VF is illegal. They are not illegal to sell or buy. They are illegal to install. That is a neat trick, don't you think?
I prefer ceramic VF to Blue Flame VF htrs. Ceramics burn much hotter than the BF's The very best vent free heater is the Rinnai 824 & 510. Modulating from 8-24kbtu and 5-10kbtu, quiet and cool to the touch. Ihave taken my oxygen analyzer and put it in the throat of the 824 and gotten 0 CO reading. Rinnai dropped the other styles VF's back in '07 once the cheap Chinese junque hit the market.