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Funnily most digital audio is never fully silent for a different reason. Noise is added for the least significant bit, because otherwise you can hear artifacts (deemed less attractive than noise) on silent parts that are close to the threshold of the bitdepth.

https://en.wikipedia.org/wiki/Dither#Digital_audio

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That's the noise floor, which should be below the threshold of human hearing unless you turn the volume up so high that the loudest signals would be uncomfortably/damagingly loud. 16-bit digital audio has a dynamic range of 96 dB. Even in an extremely well-insulated anechoic chamber where we (unrealistically) assume the ambient noise level is 0 db, you would theoretically hear extremely quiet white noise when playing back a plain old 16-bit CD, but that CD would still be able to blast out 96 dB which in nearly all imaginable circumstances would be louder than desired. In a more realistic scenario wearing well-isolating headphones in a very quiet normal room, the ambient noise level is probably more like 30 dB, and plain old 16-bit audio gives you plenty of dynamic range to perfect reproduce any conceivable digital audio signal for the vast majority of use cases. Certainly for things like music, I think it would be quite rare for a recording to have a dynamic range greater than, say, 60-70 dB.

Dither works for images too, e.g. for cheap displays that only have 5 bits of color depth. It's hardly a problem for audio anymore which is now almost universally 24 bits (and arguably already wasn't an issue at 16..).

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