Fading out at the end of a song has become something of a recording cliche, but no-one seems to know for sure why it started.
When it started is possible to track down, to the Farewell Symphony of 1772 by Joseph Haydn. At the end of the work, the musicians gradually leave the stage leaving only two violins to play the final notes. That was before the era of recording of course. Oh well, let the pedants revolt.
146 years later Gustav Holst fades out the last movement of his The Planets. It closes with a women's chorus who perform in a room separate from the main auditorium, the door to which is slowly closed.
In recording, America (1918) by the chorus of evangelist Billy Sunday and Barkin' Dog (1919) by the Ted Lewis Jazz Band are reported to end in fades.
But fades became more commonplace in the modern era of recording which started in the 1960s.
Some say that the idea of a fade is that the music never really ends, it just keeps on going. There's a certain amount of
arty-fartiness artistic sensibility in that.
Others will say that it is just the lazy person's ending because they can't be bothered to think up a proper finale for their song.
I would say that it is indeed a bit lazy. But on the other hand it could be a sign of a song that has been conceived in the studio rather than for live performance.
Other than the classical music examples above, it is impossible to fade out live. Try it and see if it works. No don't bother, your audience will look at you as though you are a pack of idiots. (Yes I tried it, around the age of 15 or so, only once.)
But there can be more to fades than just fading.
Some songs have really long fades – Hey Jude by The Beatles for example.
Also by The Beatles there is Strawberry Fields, which fades out and fades back in again. George Martin described how this happened as a bit of a wild jam going on at the end of the song. At one point it fell apart, then came back together again. So they just faded the part that didn't work out!
Creativity in fading indeed!
P.S. When Holst's The Planets was written in 1918, only eight planets had been discovered, so the work ends with Neptune. Pluto was discovered in 1930. In 2000, Colin Matthews was commissioned to write an additional movement to depict Pluto, and thus bring The Planets into line with the known solar system. Unfortunately Pluto's planetary status was canceled in 2006. Whether Matthews still gets his royalties isn't known…