Noise, it's in all systems. What you describe is when a measuring device (ears in your case) has reached it so-called "noise-floor", a minimal point where the internal noise of a system has overtaken the external sense/input/stimuli levels.

Inherently all systems generate noise. Try closing your eyes when you sleep, sometimes you can "see" little color streaks, or if you hear a surprising sound you realize your vision flashes white even when your eyes weren't open. The reason we dream is theorized as the brain's inability to interpret a lack of stimuli, so the brain starts making assumptions due to a lack of input, and that can be called noise in a way too.

But hell, i'm an electrical engineer, not an neurological theory.