Perhaps you should undertake this exercise and let us know how it sounds :)
EDIT: In my experience with audio, when I have a bug that introduces even the slightest discontinuity (or even just a cusp) in the audio, well short of a pop to silence, I can still hear a "weirdness". Ears are pretty attuned to things that sound unnatural. I'm not confident that essentially "forging" the audio is going to sound natural.
You can even hang intentionally to generate original music!
(/s, please don't)
You could maybe make an argument that it would be useful in live music settings to prevent a bad situation from sounding even worse, and maybe you'd put it on some audio software so you can sort of still enjoy playing music on a crappy system, but really, it's best to have hardware and software that can 100% guarantee keeping up with audio processing.
edited typo
Yes that's true, I'm proposing something that uses an approximation of it.
Consider it from a different angle: the inner ear essentially performs a Fourier transform. At every moment the "instantaneous" spectrum determines which hair cells are triggered. Now what I propose is to keep triggering those same hair cells (and not any others) when the buffer runs dry. The exact way of accomplishing this is left as an exercise (though using short windows where you take a FFT could be a good approximation).