What will happen to your Car if you didn't replace your old and damage Daewoo Catalytic Converter?

Your car will not run right, and could catch fire

Nothing, except it may not pass inspection.

Loss of power will be experienced as well as the possibility of a failed emissions test.

It depends of the law and regulations of each country, I removed the Catalytic converter from a Nubira 1.8 DOHC and it passed all emissions test. If the catalytic converter is too old, it raises the fuel consumption and reduces the performance. But if your Nubira has two oxygen sensor (one before the catalytic and another after the catalytic) you shouldn't remove the catalytic because it causes a DTC (Diagnostic Trouble Code) because the ECM checks the signal of both sensors.