Contributing to an existing game requires some initial involvements, clearly, especially if it's about code.
The amount of involvement can vary, depending on project's code rot (or quality, depends).
For art and quests (backstory is an art, too), I think there's also some involvement required, maybe less, but in any cases you need to know the artistic guidelines of the universe, because real games, unlike tech demos or engines, should have that: artistic guidelines and universe, more or less developed depending on the game.
Well, quests might or not be important depending on the genre, but I think even a pure shooter like doom have some universe :)
Now, I think projects which are made to be very moddable could be targets of such events, but I'm afraid I don't know many myself (wesnoth, flare, probably, others? I don't know).