When a cylinder misfires, the fuel is not burned and is dumped out the exhaust. Over time this can damage the converter because the fuel is going to burn in the manifold or converter, and the increased temperatures are hard on it. This happens 100% of the time if left unchecked, but I've never heard of it happening anywhere near this quickly. It takes quite a while to slag the converter in an older car badly enough to throw a P0420 or P0430 trouble code.
But misfires and converters are related.
2014 Sterling Gray GT Premium with silver stripes / MT-82 / Brembo / Recaro
Steeda Sports | Koni Yellows | BMR Panhard and LCA Brackets
MGW shifter | Borla S-types