This pipe is broken on my converter. What is it for? Also, could this make the car run bad?

 

It is as far as i know the A.I.R. system. pumps air into the cat to offset the exhaust so it seems cleaner. I wouldn't think it would effect anything.

 

That is the AIR line. Just like HighTechRedneck said its there to carry fresh air into the converter so it burns cleanly. There is a smog pump on the belt system that pumps the fresh air. It's not exactly needed unless you are doing emission testing, technically it's against federal law to remove such items. It's far enough back it's not going to mess with the O2 sensor reading on a 3rd gen (our O2 sensors are at the header/manifold not near the CAT).

If you're really worried about it you could probably get some exhaust repair wrap and just wrap it back together. Some rubber hose with clamps might even work. I don't know for sure how hot the AIR tube gets. I would think it's way to much work to remove it to weld.

 

Also, that is stainless steel, more work to weld it. I would leave it, or even JB Weld would probably do the trick, That air Tube shouldn't get hot enought to wreck JB Weld.

 

My recommendation would probably be more work and depends on how much tube is left sticking out from the CAT (can't quite tell from the pictures). You could get a short piece of metal tubing that is just a bit bigger and use two small clamps (basically smaller versions of what is on your exhaust pipe there in the picture) to clamp it together.

Or, I have done it with a compression fitting coupler. That requires pretty decent alignment of the two ends as well as a clean cut on each. But, it does make for a very clean looking repair.