Why?
It seems to me that as soon as you stop the instrument from making a sound at the end of the piece, it's done. I understand that the final rest is necessary to fill up the measure, but why put a fermata over it?
Do you sit there and prevent the audience from clapping until you want that rest to finish its extended duration? Do you ensure that the recording of the track of that piece has that few seconds of silence at the end?
Passage from Louis Vierne - No. 17 Lied
Do you sit there and prevent the audience from clapping until you want that rest to finish its extended duration?
I've always thought this is pretty much what a fermata like this is about. When classical music is performed, there are initial motions, playing of instruments, and final motions. Audience members who attend a lot of concerts usually understand it is considered best practice to hold applause until final motions are completed.
A classic example of a final motion for which one holds applause is when a conductor lowers their arms to their sides at the end of a piece. More relevant to this example, when a pianist finishes a piece, their final move is usually to place their hands in their lap, signaling that they are done and the audience may proceed to applaud (or storm out dissatisfied) without risk of interrupting the performance.
It may seem strange to write into the music that the pianist hold their hands up for a longer than usual amount of time before lowering them to their lap, but there is a palpable effect on the audience of this kind of action. It allows the final notes to ring in the mind, if not the air, before the (hopefully) thunder of applause takes the audience out of listening mode and into responding mode.
Re-reading my answer triggered in my mind an analogy from CDs/albums. In all genres, when you arrange the tracks on a CD, LP, tape, or whatever, one of the choices you have to make is how much silence there should be at the beginning and end of track. It's very interesting to experience how making different choices for amounts of silence changes the impact of the end or beginning of a track. There is also an impact made by how much "air" is included in a recording. Human ears are surprisingly sensitive and we often don't even realize that we are hearing a slight change from absolute silence between tracks to the very subtle noises of breathing and shifting and even air molecules hitting the diaghram of a microphone that signals to our brains that the music is about to begin. Allowing this "air" time to be longer at the beginning of a track leads to expectation and anticipation, and then to impatience and eventually frustration for listeners, even if they don't know why, and leaving some "air" time at the end provides some quiet time for thought, reflection, and lingering emotions to play out at the end of a track.
If you've ever just sat in silence, unmoving, for a few minutes after listening to a favorite recording, then you've experienced the effect of silence at the end of a piece of music is about. It is a bit of a mystery, even though we all (or almost all) can relate to it intuitively.
I've always understood it as a largely conceptual action.
I've never seen something like this at the end of an aggressive or violent movement (though if anyone has any examples, I'd love to see it!); instead, I've only ever seen these at the ends of more solemn movements (like in your example). As such, I've always viewed it as a way of crossing the barrier between music and silence that fits the solemn mood of what came before. In order to do that, the performer must extend this rest as long as s/he deems fit, given the performance environment.
Slightly related, here is a performance of the end of Mozart's Requiem with a silence of 40 seconds before the applause.
Lastly:
Do you ensure that the recording of the track of that piece has that few seconds of silence at the end?
Possible, and it's a good thought. But keep in mind that, for a lot of these composers, the notion of "recording" just plain didn't exist yet.
In some performance scenarios, for example in a church or cathedral, the sound will echo around the building, dying away after the musicians have stopped playing. This could be an instruction from the composer to allow the sound to die away, with this sound being considered a part of the music.
A possible reason is that this piece probably isn't written for one instrument, and while your part has a rest, somebody else could be playing. And it just won't look good if some of the performers start putting down their instruments while others are still playing. Also, this extended rest provides a sort of a "finishing touch"- if the players relaxed and put down their horns right after the last sound, it would look hurried and leave the audience without a sense of completion.
"The rest is silence." A subtle concept when spoken by Hamlet at the end of his play. Maybe not quite so subtle in this musical context.
The most magical moments in a piece of music are often ones of silence. The rests are as much a part of the music as the notes. This is a moment of silence AFTER the last note. A performance gesture rather than an acoustic one, perhaps. But none the less real.
Or maybe it isn't the end of the whole piece, just the end of that section. In that case the fermata rest can be taken more literally.
