I was listening to the Elvis song “Suspicious Minds” and keyed in on the part where the song faded out like it was coming to an end but then it faded in again to regular volume (starts around 3:32). I was wondering if there is a name for this and also can anyone name other songs that do this? Thanks.
A few other songs that seem to fade out then come back loud for a bit:
King Crimson’s “21st Century Schizoid Man”
The Small Faces’ “Afterglow”
“Paper Sun” by Traffic. It’s the first song on the album Mr. Fantasy. Then, as you listen,* you can hear bits of it between each song. The final song on the album – titled “We’re a Fade, You Missed This” adds a final verse to “Paper Sun.”
*On the original US version of the record; I don’t think it happens with a CD or download.
“Strawberry Fields Forever” does this, if I understand what you’re talking about.
Critical Mass from Aerosmith’s Draw The Line fades out, then fades back in again, then ends.
(It’s been a while since I’ve listened to that record, I hope I’m not remembering the wrong song.)
Usually called a false ending, though that doesn’t necessary indicate a fade either way. For example, “Come and Get It” by Badfinger appears to come to a cold ending as the singers harmonize a nice closing cadence, but after a moment of silence, the lead singer comes back in full voice with “Sonny!”
As does “Helter Skelter”.
Ray Charles’ What’d I Say ends and then comes back for more than two minutes! That’s more of a reprise than a false ending.
The Small Faces song you recall is “Long Agos and Worlds Apart,” which follows “Afterglow (Of Your Love)” on Ogden’s Nut Gone Flake."
But majors props for referencing the Small Faces in the first place! 
Kiss’ I Love It Loud?
Bowie’s Life On Mars?
Against the 70s by Mike Watt does this pretty effectively.
Let 'Em In by Wings.
Heart of the sunrise by Yes.
Not that particular type of fade, but one of my favorites, Simon and Garfunkel’s “Silent Night 7 O’clock News”. The lyrics of “Silent Night” slowly fade out while the news announcements of grim stories in the background fades in, to eventually replace the innocent song.
Dennis
Alice in Chains “Rain When I Die” does a fade out and then fade back in. I love the song, but I hate that ending. Alice In Chains - Rain When I Die - YouTube
Another example: Appropriately, “Fade Out” by Guadalcanal Diary
I thought the title track, “In The Court of The Crimson King”, was a better example of that.
Isn’t the ending of “…Schizoid…” simply a loud, jazzy free-form blow-out?
Hendrix’s “Ezy Ryder”
coulda sworn there was a Sabbath tune that also did that.
While it does feel like it’s ending, I’m not sure the pause really lasts long enough to count as a false ending. ‘Sonny!’ seems to come on the beat after ‘money’.