The substrate of a catalytic converter (AKA “cat”) is made of a fine ceramic mesh or a roll of corrugated metal. This substrate is then wash-coated with a slurry of extremely fine particles of catalyst. The fine particles have lots and lots of surface area, which is good, because that surface is where the catalytic reactions happen that turn NOx back into oxygen and nitrogen, turn poisonous CO into relatively innocuous CO2, and oxidize unburned hydrocarbon fuel into water and CO2.
Cats have a tough job, but they do it well. Engine exhaust is pretty damn hot, but they put up with it just fine.
Unless it gets too hot.
If you get an unexpectedly large amount of unburned fuel into the exhaust system (especially if it arrives with usable oxygen, as in the case of a misfire event) the cat will try to oxidize it, which releases heat. The cat was hot to begin with, but now it’s gonna get hotter. A random misfire here and there isn’t the end of the world, but sustained misfires will end up dumping a lot of heat into the cat. The ceramic or metal substrate can take quite a bit of heat, but the tiny catalytic particles have their limit. They are in contact with each other on the surface of the substrate, and at some point, they start to melt and sinter together: where they once had point contact with each other, they begin to have area contact, and end up with much less total surface area exposted to the exhaust gas. With this reduction in catalytic surface area comes a reduction in effectiveness: pollutants pass through the converter unconverted. There’s no recovering from this: once those little particles are sintered together, you just have to replace the cat.
The cat can also be coated with “poisons” which prevent direct contact between the catalyst and the exhaust gas. Lead is one of them, and that’s part of why lead was banned from automotive fuels a few decades ago. Silicone-based lubricants can do the same thing. ZDDP is an engine oil additive, the zinc and phosphorus in which are cat poisons; successive API classifications of motor oils have placed tighter and tighter limits on the amount of ZDDP that may be added to the oil so as to prolong the useful life of the cat in later model cars.
As a car owner, what can you do? Cars are pretty smart these days; they keep an eye on themselves, and will let you know if something comes up. If the “CHECK ENGINE” light comes on, don’t ignore it! Most auto parts stores have a scan tool and will read your car’s fault codes for free (they figure you’ll probably buy parts from them). If your fault code(s) indicate a misfire or a faulty oxygen sensor (in which case the engine control computer often defaults to a rich mixture), get it taken care of pronto. Again, the occasional misfire won’t wreck things, but “occasional” often becomes “frequent/constant” after a while, and that’s when you start to do damage.
As far as lead goes, don’t worry about it; leaded motor fuel just isn’t available these days at your neighborhood gas station.