Well, it's not quite that extreme, but in Tangent Knights, I created the character of Spark just because I wanted to fill out a team that homaged the typical team composition of late '90s-early '00s Ultraman shows and needed someone to play the role of the cute young communications/tech officer. She ended up becoming an unexpectedly important and rich character in a variety of ways.
Nancy Conlon was just an engineer that Dayton Ward & Kevin Dilmore created to be the person who finished up a task for Duffy in Interphase Book 2. She didn't have a first name or dialogue in that initial story -- if Starfleet Corps of Engineers was a TV show, she'd have been played by an extra, if she was ever even on screen. She wound up becoming chief engineer after saving the ship in Wildfire and later became chief engineer on Voyager and a somewhat major supporting character in the Voyager post-finale fiction.
Thanks. Glad I'm not the only one. In my case, the character is the protagonist's beloved aunt -- her dad's kid sister. Created for the specific purpose of giving her big brother (i.e., the protagonist's dad) a motivation, in the form of a severe case of "Prodigal Son's Big Brother Syndrome."
For that matter, what you describe is pretty much how the character of Damar evolved on DS9. He was just a guy Dukat gave orders to when he first appeared, and look at what he turned into.....
Or O'Brien. Colm Meaney started out on TNG as a bit player who showed up as various nameless background characters, and then in season 2 he settled in as Transporter Chief, eventually gaining a surname. And look where he ended up.
Another detail (and why I mentioned "nothing more than on offhand reference to somebody the readers don't ever actually meet") from my own opus-in-progress: in the original throwaway reference, the protagonist's parents were arguing over whether she should be allowed to have a particular apparel, something to the general effect of: Mom: "Your sister practically lives in [apparel]!" Dad: "[kid sister]? Now there's a great role model. And I suppose that if [protagonist] wants to smoke marijuana, that's ok, too." Mom: "You know she gave that up when she started taking flying lessons." Later, the beloved aunt/prodigal sister character makes an appearance, announcing that she's taking the family out to dinner to celebrate a promotion (that Dad assumes was a reward for sexual favors). And then, in the present draft, I introduce the character (without an actual appearance) when the not-quite-two-year-old protagonist sees an organ for the first time, and it seems like a cross between a piano and the controls of one of the airplanes her aunt flies. So in my scenario, what turned out to be a very interesting supporting character literally came out of an offhand bit of throwaway, meant to establish "Prodigal Son's Big Brother Syndrome" as a motivation.