The problem indicates that there must have been a problem with the catalytic converter. When catalytic converters fail they normally clog up with debris and block the flow of exhaust gas from getting out of the system. A totally clogged converter will eventually cause the engine to die due to increased backpressure. Usually the only way to tell if a catalytic converter is clogged is to remove it and check the change in engine performance. When a mechanic suspects a clogged converter they may remove the O2 sensor from the exhaust pipe and see if there is a change in performance.
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