Are there RPGs where some of the character creation is partly done during play?

[Joe the Rat]

One wrinkle on Dread is that if you don't succeed, you're going to die. Like Traveler.
Freeform and story-driven tend to work well with this. The trick is that you start getting away from "character creation" beyond what's needed in narrative, and likely not evolve past the story.

I can think of another sort-of example: Munchkin. Race and Class may come (and go) over the course of play. If only there were a way to harness that system for good...

Total sidebar here... but I find the acronym FAE amusing

Consider that it is short for [Fate Accelerated Edition]... and FATE was originally an acronym itself, which was short for [Fudge Adventures in Tabletop Entertainment], based on the older Fudge RPG. Going even deeper, FUDGE was originally an acronym too [Freeform Universal Do-it-yourself Gaming Engine].

So FAE is an acronym nested in and acronym nested in an acronym.

Oh dear I've gone crosseyed.

Freeform Universal Do-it-yourself Gaming Engine Adventures in Tabletop Entertainment, Accelerated Edition

You only wish your game's title was this long and descriptive.