In the deep, far future, at the time of the "heat death" of the universe, if I turn on a radio will I get the sound of static or of total silence?
I'm by no means an authority on this subject. At best I'm an enthusiastic amateur, so take my answer with a bucket of salt.
The static on the radio comes from the redshifted heat of the universe expanding. Even if all energy in the universe has evened out, the expansion is still going on, creating the redshifted heat.
However, so much time will have passed that the distances involved will cause this redshift to be even greater. At some point this static will be on a spectrum too low for a radio to pick up.
Also, even if you were able to tune your radio low enough, as the static is now created outside of the observable universe, there's no new noise that can reach you.
Ergo, silence
And the universe's expansion is accelerating, so even if you have the most sensitive receiver that can pick up very low frequencies, at some point the waves will be stretched so thin that they'll be essentially nothing. Of course they won't be zero, but where you draw the line for "essentially zero" is up to you.
Not all radio noise is from the CMB. There's also thermal noise, though this would be minimized too if our hypothetical radio at the end of time is near absolute zero.
If we're going that far, then no radio or person either. Black holes have disappeared from Hawking radiation, protons have all decayed, and the distribution of energy is so even and so rarified no exchange can happen, so literally nothing can happen.
If we allow a magic radio, we can allow a magic air bubble.
In the unimaginably vast and vacant void, a single plain white half-dome radio drifts, aimlessly.
The eons stretch onward, silence fills the universe.
When the last vestiges of everything have finally ceased, and the universe at last becomes one with nothing, a single, dim, red light inexplicably flickers to life.
A speaker crackles to life, a soft but angry voice emanating from within and stretching across the abyss.
"Hello Dave. It's been a loooong time."
This thread and comment bring to mind Isaac Asimov's short story The Last Question.