2000 Chevy Malibu exhaust system

We had a blowout in our exhaust system. It happened between two (bubbles?) In the tailpipe. I assume one was the Catalytic converter while the other (I was told) was the resonator. The shop we brought it to said the repair was no problem to patch a new pipe in between. What he did was cut from the joint between the two bubbles to three feet back and weld a straight pipe in. He left the front bubble intact. I'm assuming he left the O2 sensor in because the engine light isn't on, but there is a noise issue (loud pipes). Is there a problem with what he did? Is it a legal alternative (I live in Michigan) to have the exhaust set up in this way? Thank You! Also He never showed my wife the old parts or explained why he removed them. Isn't it the law to do that?