I do not believe a mass extinction event could reverse the effects of climate change, killing many humans and destroying machinery would slow it but not reverse it.
Also, natural reversal of climate change might take far too long in your world, long enough that humans may have died out as a species.
However, you did mention the stabalisation of climate change. If you wanted a natural event to wipe out a large portion of the human population, you have several options. Im going to rule out volcanic activity as that would add sulphur and carbon into the atmosphere, adding to climate change. So then the next most plaussible options are earthquakes and tsunamis. If an extremely large earthquake ripped accross a major industrial country, it would destroy machinery and slow down climate change due to factories being destroyed. A similar thing would happen with tsunamis, causing major loss off life and damage to factories.
Although, if your world is sufficently advanced, a major solar flare could be devastating. If your factories, industries and power plants are automated by robots or use highly technical machinery, a solar flare would majorly disrupt and damage electronics, halting all of the world’s automated machinery. This would also reduce the growth of climate change as now no harmful fumes are being pumped into the atmosphere. If your cars and public transport were also automated to some degree, they would also be majorly affected and may cease functioning, further reducing the fumes going into our air. As an aside, this might produce a beautiful aurora borealis across the world.
Many humans would be killed indirectly as a result of the solar flare, planes would fall out of the sky, ships may run aground, trucks and cars may lose control and cause crashes, powerplants and factories may go critical and explode, hospital equipment may cease functioning just to name a handful. I would not be able to give you an estimate of the loss of life but, suffice to say, it would be significant on the global scale.
In terms of the socioeconomics of your world, they may be completely decimated by the flare, preventing all trade and communications. All forms of transportation would no longer work and goods could not be transferred exept by foot or transport that has no electronics.
In conclusion, a solar flare against a sufficiently advanced society, not too far from earth’s own technology, would be devastating for any electronics. Automated factories and powerplants could immediately halt production and irreparable damage may be caused. Cars and trasnportation may also cease functioning and further reduce emmissions into the atmosphere. The effects of the solar flare may revert humans to a pre-industrial state and allow for the stabalisation of climate change.