I just got a used 2001 Elantra with a cracked flex pipe--local shop wants to replace whole piece from flex pipe back including catalytic converter, says it's one piece--is this true or can the flex pipe be inserted and the original converter kept?

 

It is not one piece on my 1997 Elantra. The layout changed in 2001.. but I don't think it went to one piece. Crawl underneath and have a look. Follow the exhaust pipe from the front of the engine to under the car, and beyond. Every time you see a flange with bolts on the pipe assembly, it represents a new connection.
I can't think of any reason to replace the cat. unless there are symptoms indicating it needs replacement.

 

Replacing my 2nd flex pipe on 03 Elantra. my cat still good - 20 yr. old OEM part. careful buying junk new cats and run as fast as you can from shops that want to replace everything.

 

bernds post was from 2008, but still holds true today.

There are good shops out there,we just have to find them.

A little side note, some exhaust systems rust badly and do require all pipes to be replaced. Usually the converters can be reused, however.
The pipes are thin tubes that exposed to heat and moisture rust pretty quickly, not unusual.

From working with all kinds of exhausts systems , sometimes you can't save anything but the converter and all the pipes have to be replaced because the minute you start touching them they break and now have to be replaced.