Hopefully this didn't happen to you. No personal experience in this area, but have heard, that if an exhaust system is left open, the heated exhaust valves get a thermal shock when the engine is turned off and cold outside air contacts them. If the compression in the cylinders has been affected, problems would extend beyond just repairing the exhaust pipe.
------- Moralistic preaching about "closing the barn door after the (farm animal of choice has already left)": That would be a good example of why it pays to fix small problems promptly. If something goes wrong and one just keeps driving the car, additional damage can occur. If the flex pipe was damaged by worn motor mounts, that's another example. If you replace the exhaust pipe with a genuine Toyota part, you'll find the whole "mid" section is one piece = expensive part. Have heard of people having a muffler shop weld in the broken part for lower cost, which could be OK, but generally, when replacing parts is far better to stay with factory pieces. Other things that kill Toyotas: Neglecting a small radiator leak Never checking the oil level
----- Driving the car while it "skip(s) and hesitate(s) a bit" probably just damages it more slowly.
------------------- Helpful hint (in case you've got expensive engine problems and wind up buying another car): Sometimes, if you get the problem diagnosed quickly - it may not be "life threatening", and you can wait a while to save up, but generally it is best to fix things promptly and keep up on all the maintenance items if you want the car to last a long time - which is the cheaper long term than expensive surprises.