2000 Chevy Silverado Battery Draining

Hello We own a 2000 chevy silverado we have recently installed a small stereo system in the truck since doing this we have had to replace the battery twice and are going on our third one. Just to give you a little aspect on what happens before the voltage drops to 11 and the lights get dim or go out and the gages quit then finally the truck loses power. We have tried disconnecting the system and it still happens! We have also noticed that when the truck is not turned on and the key is not in the ignition all accessories continue to work as if the truck was turned on. We can not figure out the problem! We have replaced terminals and batterys and had the altenator tested and it doesnt help any help you can give would be greatly appreciated thank you amber and david parker