many indie games expect play groups to do some of their own design work as part of play.
Two examples that I thought of straight away.
In A Wicked Age has beautifully clear procedures - it is as close to "complete" (in
@gorice's sense) as any RPG I know of. Each session begins by choosing - by way of group consensus - one of four "oracles" (Blood & Sex, The Unquiet Past, A Nest of Vipers, God-Kings of War), then dealing 4 playing cards to select four of the 52 options under each oracle. Each of these is a short phrase (maybe five to twenty words) describing a person or a place or an event (or maybe more than one of those) that fits under the oracle's broad theme.
This done, the group then goes around the table, taking turns to build up a list of characters from those oracle entries - some are explicit (like if the oracle entry mentions a person) and some are implicit (like a place might imply an occupant, or an intruder, or an invader, or whatever). Then each player chooses which character will be their PC, and the rest become NPCs under the GM's control.
There is then the process of assigning character attributes. And then, if any character has a "particular strength", that has to be designed. As per the rulebook (pp 4-5),
Choose whether your character’s going to have a particular strength. If she is, choose and list it now. Choose one that already exists or name a new one – you’ll get to create it in just a minute. . . .
Particular strengths are unusual skills, magical arts, innate powers, allies, and treasures that characters can have. As you play you’ll create a variety of particular strengths for your various characters. . . .
Give the strength a name.
Describe the strength. You may be able to copy its description straight from the GM’s story sheet.
Describe the strength’s special effects: what it requires, and how it appears in action.
There are then rules for the mechanics of building a particular strength, and a couple of examples. The last time I played this game, we had four characters with particular strengths: the PC illusionist's illusion magic, the PC courier's skill with horses, the PC warlords treasure chest, and the NPC champion's Spear of Power. As this was not part of an ongoing campaign, but was a one-off, we had to build all these from scratch. It probably took 10 minutes or so. All of them came into play during our two hour-ish session.
The other, and contrasting, example is Cthulhu Dark. This is an "incomplete" RPG. Here is the core of its action resolution procedure (pp 2-3):
To know how well you do at something, roll . . . your highest die shows how well you do. On a 1, you barely succeed. On a 6, you do brilliantly. . . .
If someone thinks it would more interesting if you failed, they describe how you might fail and roll a die. . . .
If their die rolls higher than your highest die, you fail, in the way they described. If not, you succeed as before, with your highest die showing how well you succeed.
Why I say this is incomplete is that it doesn't tell us how to decide what follows, in the fiction, from barely succeeding or from doing brilliantly. The group has to bring this from somewhere else. I use "intent and task" when I GM this system, as that works well for the sort of no-myth approach that I prefer with Cthulhu Dark.
I'm not sure if either of these examples fits what you (
@Campbell) had in mind, but as I said are the ones I thought of straight away.