A repeated misfire is a death sentence to a catalytic converter.
Under normal, closed loop operation, the ECM constantly adjusts to make sure that nearly 100% of the oxygen is consumed each time the engine fires, but without using any extra fuel than necessary (most of the time).
Occasionally the engine will run rich for certain reasons (warm-up period, power enrichment, etc.) but this doesn't really harm the catalytic converter, just briefly increases carbon monoxide emissions. The reason this doesn't harm the catalytic converter is because there isn't much oxygen.
Likewise, running lean generally does not cause a long-term issue (just some short-term NOx emissions) because there isn't any excess fuel to burn, even if there is excess oxygen. Hence why Deceleration Fuel Cut-Off (DFCO) doesn't burn up your cats.
Meanwhile, a misfire sends both unburnt fuel AND excess oxygen to the catalytic converter simultaneously. At low power, this generally just heats up the catalytic converter to a much higher temperature than it should be, which shortens its life. At higher power, the catalytic converter heats up past the ignition point of fuel in air and causes the fuel-air mixture to detonate upstream and inside the catalytic converter.
Tha detonation plus the fact the substrate is already at an excessively high temperature (higher temperature weakens the materials temporarily) causes the catalyst substrate to fracture and spall and eventually either clog the cat or self-gut.