Good automotive diagnosis, like medical diagnosis, often comes down to the technician's ability to separate cause from effect, to look at a fault and determine whether or not it's a problem in and of itself or just the symptom of a larger problem. Such is the case with misfires of any type. While the inexperienced diagnostician might simply assume that an external fault is the cause, that may not be the case.
A catalytic converter is a kind of blast furnace, an incinerator designed to convert certain chemicals to other chemicals under very high heat and pressures. Most converters have two chambers. The first catches unburned fuel from the engine and burns it, creating an afterburner-like heat that facilitates the second reaction. The more unburned fuel goes through the converter, the more intense the reaction and the more heat comes out.
A misfire is the failure of a cylinder to fire, either because there's no spark, or because there's an excess or deficit of air or fuel. The odd thing about misfires is that, regardless of the cause, they'll almost always result in an increase in catalytic converter temperature. A "rich" misfire resulting from air blockage, a leaking injector or a malfunctioning ignition system will send unburned fuel through the pipes, which spikes converter temps.
A vacuum leak, clogged injector or loss of fuel pressure will cause a "lean" misfire, where there's not enough fuel in the cylinder to sustain ignition. Since the flame front can't sustain itself in the cylinder, it'll often send unburned fuel out through exhaust valve. Since converters specialize in burning away fuel that the engine couldn't, even the small amount present in a lean exhaust may well result in overheating.
The average converter's ceramic matrix generally operates at between 700 and 900 degrees Fahrenheit, and can withstand in excess of 1,000 degrees. Temperatures higher than that will crack the converter's ceramic matrix, causing it to collapse in on itself. This collapse ducts the remaining gases through ever-fewer channels, what causes a cascade effect of destruction known as "converter meltdown."
This is a chicken-or-the-egg scenario; the melted converter hasn't caused the misfire; rather, the preexisting misfire is what overheated your converter. That's not to say that your converter didn't have a few issues before -- particularly if the engine has a history of misfiring -- only that the misfire almost certainly performed a coup de gras on what was left of your converter's matrix.
