This is something I mostly associate with nursery rhymes and songs that use a specific melody repeated over and over.
An example, from a version of London Bridge Is Falling Down:
Build it up with wood and clay, Wood and clay, wood and clay, Build it up with wood and clay, My fair lady.
is later repeated over the same melody as
Build it up with iron and steel, Iron and steel, iron and steel, Build it up with iron and steel, My fair lady.
Now, the change from a monosyllabic word such as wood to a two-syllable i-ron, makes the verses longer, and as all the other pieces of the verse stays in their rhythmical places, the longer word is sung as a duplication of the same note, like a quarter note becoming two eighths.
It can also work with two extra syllables working as a triplet, or in the other direction (a verse becoming shorter losing syllables).
I know this is part of prosody, "the way the composer sets the text of a vocal composition in the assignment of syllables to notes in the melody to which the text is sung", but I can't find if there's a proper name or research around this particular variation.
Any help? :)