I have a 1977 Buick Riviera. The muffler and part of the cat back pipe have rotted through and fallen off. I know I can go to a muffler shop and have an exhaust custom built, but I really don‘t want to spend a lot of money since I don‘t have it. Do I have any other options?
O.E.M. replacement mufflers from your local parts store are not as expensive as you might think (replaced the muffler on my '87 Ranger for around $20). And a new tail pipe shouldn't cost you an arm and a leg at a muffler shop either. The problem with getting a used exhaust system from a junk yard is that you really don't know how long they will last.
Get a used muffler from a junk yard, and have them fix the pipe at the shop. That should save some cash.
Go down to your local automotive salvage yards (junkyard) to buy replacement parts for your exhaust system. Compatible GM models are very easy to find at most yards. About a week ago I bought an entire exhaust system (except manifolds) for a friends car (1989 Camaro) from one of my local junkyards for only $35