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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.
Maybe we have the radio equivalent of a Boltzmann brain
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.
THERE IS AS YET INSUFFICIENT DATA FOR A MEANINGFUL ANSWER