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.