Yeah, but... this is the leadin to a discussion of Laplace's demon. The signal isn't destroyed, but its information content can easily be made VERY hard to find. Since the uncertainty principle became established, we've been really clear that information in a signal can become meaningless added to thermal noise.
A whisper doesn't carry far, we all know. The reason, is that without the low frequency part of our voices (the formants), the rest of vocalization is such broadband high frequencies that thermal noise in the atmosphere masks it. Yesterday's whisper is no longer audible.