Doing some exhaust work on my truck. Pipe broke just before the muffler. But as I work on that, I noticed a little rubber hose that runs to the catalytic converter. What is this, and is it important to replace/repair?
No rubber hose routes directly to any catalytic converter. Some vehicles use a steel tube, it connects to a nipple on the cat converter by way of a clamp.
Since you failed to mention what year/engine size your truck is, I cannot tell you which rubber hose you are refering to, but it's prolly part of the T/E = Thermactor Emission system.
T/E = smog pump.