Songs where the lyrics for the verse are sung over the chords for the chorus (or vice versa)

for instance, towards the end of Heartbeat, Annie sings through the chorus a few times and then (with no change in chord progression/key/tempo) she repeats the third verse of the song, altering the melody to suit the chord progression of the chorus.

is there a term for this technique? and what are some other songs that do this?

I think "Quiet" by the Smashing Pumpkins qualifies - the "behind me, the grace of falling snow" part. fourth verse over chorus chords but different words.