This War of Mine.
No, it's not really a set story, but the story is written by your actions and it can be quite powerful.
One of the first things to happen to me while playing was that I came across a soldier who was obviously about to rape a civilian. I threw caution to the wind and tried to stop him. It was futile, however, as he was much better armed. The young man I was playing was one of the most upbeat and hardiest from my community of survivors. After his death, morale dropped and everything started to fall apart. No one wanted to do anything but sleep. Everyone wasted away.
To my shock, the last member of my team hung himself.
On my next play-through, I ran across the soldier and the girl again. I waited until he took her to the back, grabbed as much food as I could, and left. This sent the character I was playing and everyone else on the team into depression. However, they survived. They made it through until the cease-fire, though, obviously, not without scars.