First of all, there's over two dozen fault codes related to oxygen sensors and catalytic converters, and they mean very different things, but there is no fault code that says the converters were clogged. In fact, fault codes never say to replace parts or that they're bad. They only indicate the circuit or system that needs further diagnosis, or the unacceptable operating condition.
Since you found them to be empty, you know there is no change taking place in the composition of the exhaust gas flowing through them, and that WILL set a fault code. I'm guessing you got a fault code related to "catalytic converter efficiency below threshold".
I don't have any vehicle history or any observations or clues to go on, so this is strictly a guess. There was a spark-related misfire and someone ignored it and kept on driving. The unburned fuel going into the exhaust system would burn in the catalytic converters where it would melt the catalyst and turn the housings orange. Based on your observation the engine runs okay without the exhaust connected, we can guess the catalyst material is in the muffler and blocking free gas flow.
You're going to have to replace the converters so those fault codes don't keep on setting. When the system is working properly, the front oxygen sensors will switch between "rich" and "lean" about two times per second. The sensors after the converters will switch perhaps once per minute or two. As the converter's efficiency goes down, the switching rate of the rear sensors speeds up and approaches that of the front sensors. Those switching frequencies are what the Engine Computer looks at to measure the converter's efficiency. With no catalyst material in there, the front and rear switching rates will be identical. The computer will suspend any other tests that rely on oxygen sensor readings for comparison, so some potential other problems may cause running problems but won't get detected. With the Check Engine light already on, you'll never know if a minor new problem gets detected that could turn serious if it's ignored.
Wednesday, August 12th, 2015 AT 9:03 PM