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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
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.
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.
Agreed
Finally some peace round here.