Only plants would, but then they would exhale O2 so then we'd have O2 again.
O2=Oxgen
Now wait, how would we end up with an Oxygen-less atmosphere? I'd imagine that the process of replacing the atmosphere with something that isn't Oxygen would result in genetic mutations preferring lifeforms which breathe other things.
Unless we're talking about having no atmosphere at all, in which case only the Glorious Robot People of the Democratic Republic People's Free Union of Socialist Robots (DRPFUSR) would survive.
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