inhibit pin high without power?!

Ok, ok... I was trying to give as much information and background as I could - perhaps I could have been more succinct and saved some confusion!

My question is not really how do I have the inhibit pin high when there's no power; I understand that this wouldn't work. But when there's absolutely no power to my circuit, the 4052 allows current to flow between inputs/outputs which means I'll get sound coming out my speakers from and and all input sources. I've proven that this happens in a test circuit, and is not good.

I was really asking for alternative solutions, hense my direct question about using transistors.
The real requirements is that the outputs (two of them - L and R) from the 4052 should be blocked when there is no power, but allowed when there is a supply. This part of the circuit needs to not interfere with audio signals. So finally, my question is what is the easiest / cheapest way to achieve this?