Games where events happen and unfold outside of the protagonist's story

Watching the older demo gameplay of BSI and hearing Levine talk about it made me wonder if there were any games where the story the player experienced and the story of the game's world act independently of each other. For example, depending on the amount of time it takes to get to a certain section in the player's story, you would be facing a different set of enemies and conflicts compared to those that you would experience if you arrived earlier or later to the same event due to the story's non-reliance on the player pushing the world's events forward.

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I've only really seen this in rpgs like ff9 where Steiner's sword needs be reached under 9 hours or something like that. It would be interesting to see events unfold differently depending on how the player performs, but the lazy option is always a difficulty slider with increased enemy damage and health. It's not something that can really sell a game on its own. The rest of it will have to be good as well.

CrowbCat is cool and good.

If you go back to old areas each day in Custom Robo: Battle Revolution you'll find a lot of the NPCs have their own stories that unfold.

Dead Rising 2 (only one I’ve played) has a timeline. Not going to X location(s) to save Y person(s) will cause you to be unable to “win” the game properly.

Majora's Mask is based entirely on the fact that shit happens to the townsfolk of Termina, even when Link isn't around to take part in those events.

That happens on Pathologic.

Thanks for reminding me, I forgot that all of the Dead Rising games (Except 4) had timelines in them.

Also, I remember hearing that the recent releases of Cave Story are suppose to have a new "good" ending, but it's only achievable if you reach Toroko in less than 10-15 minutes the moment after she is abducted (With this clock not stopping even for cutscenes). Is there any truth to this?

Original Fallout 3, aka Van Buren