What happens when you hook a sub woofer to your regular speakers in 1996 Chevy Lumina and the radio Goes out?

In 1996, it was not common practice to connect a subwoofer to a factory car stereo. If a subwoofer was added, it was typically done through an aftermarket amplifier and wiring, bypassing the factory radio completely. Therefore, it is unlikely that adding a subwoofer would cause the radio to fail.

If the factory radio failed after some kind of modification to the audio system, the most likely cause would be an incorrect wiring job, such as a short circuit that blew a fuse.