Rush did it in Double Agent, on 1993’s Counterparts album.
“The Letters” by King Crimson. Boz sings the last lines unaccompanied.
Well it goes back at least as far back as 1968;
Crown of Creation - Jefferson Airplane
I believe Vance Joy’s “Riptide” is also an example of this phenomenon.
Is the OP referring to “Stop time” songs, like Hoochie Coochie Man, Seventh Son, Further On Up The Road, etc.?
The Band Perry does it in If I Die Young.
No. Listen to the OP’s examples. He’s talking about songs where the ending consists of the band completely dropping out (all instruments including rhythm tracks) and ending with a bare vocal.
Here’s the ending of “Shape of You” to give you an idea.
Here’s the Taylor Swift song cued up to the end.
And here’s “Despacito”, with the title being sung unaccompanied as the last notes in the song.
Crap, missed the edit time to fix the last link:
And here’s “Despacito”, with the title being sung unaccompanied as the last notes in the song.
“I love ya, hon-aaaaaaaaaaaaay!”
Does the Cranberries “Dreams” count? (voice over fading bass sustain & random tom-tom)
(Damn, still too soon. Got me all verklempt.)
I could’ve sworn this thread was more recent than this, but here’s a sad bump two years later: “Stacy’s Mom” by Fountains of Wayne ends with just “mom.”
A less-sad one IRL, but (spoiler alert!): “Everything You Ever” from Dr. Horrible’s Sing-Along Blog. Ends with “a thing.”
Float On by Modest Mouse.
Black Water by The Doobie Brothers.
Can’t Stop by Red Hot Chili Peppers
Pat Benatar’s Heartbreaker. Also You Might Think by the Cars.
“Tequila!!”
The Champs, 1958
LOL, I watched the follow up video to The Taylor Swift one, Katy Perry’s Dark Horse, and it has one too. (There is sort of an echo at the end so I don’t know if it exactly count).
I do think it’s prevalent now, I also read that fade-outs have fallen out of favor, whereas they were almost ubiquitous in 80’s music.
There’s even more if you count parts where the drum beat continues with the vocals while other instruments stop.
“Old Time Rock and Roll” by Pete Seeger and “Mountain Music” by Alabama come to mind. “We Will Rock You” by Queen does it backwards.
I think you meant Bob Seger. 
…and another. The album version of Come on Eileen by Dexy’s Midnight Runners.
This doesn’t add a lot of value to an old thread, but I was convinced I was right about this, and had to go find the damn thing just to prove it to myself. So, Dammit, here it is.
Actually, it’s rather good.
j