Why a random misfire code that is followed by a catalyst-efficiency code usually points to misfire aftermath, not an isolated converter verdict.
When P0300 shows up first and P0420 appears later, the timeline is screaming for attention. That sequence often means the converter was exposed to misfire fallout before the catalyst monitor finally complained. The converter may be truly damaged, but the order of events tells you not to start with the converter as if it failed in isolation.
A misfire sends oxygen and unburned fuel into the exhaust together. The catalytic converter then has to process a combination it was never meant to digest in large amounts. That can overheat the substrate, contaminate it, melt sections of it, or simply push monitor data out of bounds for a while. In other words, P0420 after P0300 can be real damage, temporary catalyst stress, or both.
If the engine is still misfiring, still running rich, or still flashing the MIL under load, stop treating P0420 like the main event. An active upstream problem can keep producing misleading catalyst-monitor data and can destroy a replacement converter just as efficiently as it damaged the old one. The first win is a stable engine, not a faster converter quote.
The pattern gets stronger when you also have a recent rich code like P0172, obvious fuel smell, black smoke, a rotten-egg exhaust odor, or a history of driving with a flashing check engine light. It also gets stronger when the car misfired hard enough to shake, lose power, or trigger post-refuel EVAP-rich clues such as P0441 or P0496 before the catalyst code arrived.
That usually means one of two things. Either the converter survived the original event poorly and now really has reduced oxygen-storage capacity, or the catalyst monitor needs more clean drive data after the upstream repair before you know whether the code will return. Clearing everything and immediately condemning the converter is a lazy answer when the engine only recently stopped misfiring.
Freeze-frame, mode-six misfire counters if available, fuel trims, and upstream-vs-downstream oxygen behavior all matter here. If trims are still ugly or misfire counts are still climbing, the upstream problem is not finished. If trims look normal, misfire counts stay quiet, exhaust leaks are absent, and downstream oxygen tracks too much like the front sensor across repeated tests, the converter itself becomes a much stronger suspect.
P0420 is Bank 1, P0430 is Bank 2. On V engines, ask whether the original misfire was bank-specific or broad. A one-bank catalyst code after one-bank fueling or ignition trouble makes sense. Dual-bank catalyst codes after a broad P0300 or severe rich event suggest the whole exhaust system lived through a bad day, not just one isolated sensor glitch.
Most of the time, P0300 followed by P0420 means this: the misfire came first, the catalyst suffered second, and replacing the converter before proving the engine is now healthy is backwards. Confirm the misfire and mixture story is truly over, verify there is no exhaust leak or sensor lie, and only then decide whether the converter was merely stressed or permanently damaged.