When the game begins, the player character is a young man. The player has been playing for a while, reaching no satisfying end point, when he is approached by a man with a fancy suit and very neat hair. As the man comes close, the camera shakes a tiny bit, the music repeats a note, and the gameworld (including everything and everyone in it) freezes. This glitchiness lasts no longer than one second. Suddenly the character is in his bed. The player gets up, walks past a mirror on the wall, gets dressed and goes out to continue the game.
All the other characters are speaking about things which the player has not seen. They talk to the player character as though he is meant to understand what they are talking about. The player is given vague clues that it's been a few months since the last scene, though it's a bit early to give it away entirely. Otherwise, the game proceeds as normal.
Then the man in the suit walks toward the player character, the game glitches for maybe a second and a half, and he's back in bed.
..and so on. The first segment of gameplay (before the first appearance of the man in the suit) is fairly long, but each successive segment is shorter. The glitching is slightly longer each time, where by "glitching" I mean that the camera gets stuck between two points, the game freezes, and the music loops whatever the last second it played was until the character is back in bed. Each time, the character gets subtly older in appearance, though this is so subtle that the player might not notice for a while.
Another change over the course of the game is that the man gets progressively harder to spot. The game might freeze at the moment you see him sitting in a chair across the street. Or it might freeze as you're minding your own business as he walks around a corner far away. One time the man knocks into you, then walks away, five seconds pass, and then the game glitches. But that's a one-time gimmick; more often the player is likely to not have even noticed the man in the suit, because he is just wandering around in the background.
Sometimes the player wakes up and discovers that an important character has died. Sometimes the player wakes up and discovers that what the goal he's been playing toward is already irrelevant. Sometimes the player wakes up and discovers that the game world has changed significantly.
By the end of the game, the player is playing an old man. The glitches last a good ten seconds, and the player can barely get in five minutes of gameplay before they happen. He stumbles out of his house after one glitch, and there's a huge crowd outside. There's nothing to do in the crowd, but the player's actually safe there. As soon as he leaves the crowd and walks into some secluded little alleyway or house (it doesn't matter where), he sees the man waiting there.
He wakes up, gets out of bed, and before he can even get to the door the game freezes again. Again the player gets out of bed, and he doesn't even make it that far. And so on, until the game crashes immediately after the character wakes up, his eyes wide open in fear, and that glitch holds. It doesn't matter if you leave the game running for hours, it's going to keep looping the music and shaking the camera and not accepting input. There are no end credits; the only way to end the game is to shut off the console.
When the player goes back in, he discovers that his save file has been deleted.