Ok, I'm going to write a story. This story will have a lot of elements which will help to define the world. The key is, some of these elements may contradict any plot you may have, or go against the "nothing" idea, the limitations of your engine, or whatever. So after reading, feel free to go "no, don't use that, because XYZ" and that will help narrow in on what you really want.
Bill was startled from his sleep, first by a loud crash, and next, by a piercing alarm. Sure, it was almost noon, but he still didn't like being disturbed. He rose out of bed and rushed to his apartment window. At the end of the street below, he could see a rusty powder blue convertible, its hood crushed by the hydrant which was now shooting a fountain of water across the road. As Bill looked closer, he noticed there was no one in the driver's seat. He glanced around -- the street was completely empty. Other than a bright red minivan parked outside his complex entryway, all he could see were some newspaper pages fluttering by, caught by the wind. Bill went to call the police, but upon dialing the operator to get the local police station, no one picked up.
Confused, Bill decided to head down and check out the scene. He grabbed his jacket and headed down the hall. On the floor below, he passed his downstairs neighbor's door -- it was open. In the hallway, he saw a bag of groceries spilled out, and a sun dress piled in a heap, a sandal poking out from beneath. He poked his head in the door.
"Hello?" he called out. "Mrs. Miller? Anyone home?" He glanced around the apartment. There was a shirt and a pair of slacks laid out over the couch, and a tv was playing an old Twilight Zone episode, a man who finds himself the last survivor on earth.
Bill backed out of the room, and continued downstairs. After reaching the ground floor, he opened the door and stepped out to examine the scene. In the front seat of the car he found a suit and shoes, soaked from the hydrant leak. Bill looked around. The playground across the street, usually filled with kids, was empty, the wind blowing a swing or two back and forth a bit. He turned back, and noticed the red minivan was no longer parked outside.
Bill walked over a block to the nearby hospital, checking to see if maybe the driver was taken there after the crash. This was more interesting than looking for a job for the 12th day in a row. He walked through the automatic doors and was met with dead silence. Not a soul was in the hospital.
He began walking the halls, looking for a nurse -- a janitor -- ANYONE. Nothing. Suddenly, he saw a shape move past a window. He turned, but it was gone. Moving around discarded gurneys and the nurses station, he entered the maternity ward where he saw the shape through the glass. He found nothing - not even any newborns. The lights began to flicker, then went out. Bill quickly found his way out of the hospital. His stomach growled, and he remembered he hadn't eaten since last night. He headed over to the convenience store.
He was met yet again with an unlocked and unstaffed location. He walked down the aisle, looking for his favorite snack. As he reached the end of the row, he heard a crash. He turned, and saw a broom had fallen over and knocked down a display. He inched closer to the broom, slowly. As he reached down to pick it up, a rat jumped out from beneath the display, and rushed for the door. Bill clutched his chest and fell backwards. Muttering a few choice curse words to himself, he stood up, brushed himself off, and headed outside. He left a few dollars on the counter before leaving, figuring that would cover the snacks.
As he stepped outside, clouds began to roll in. Rain began to fall, and the sky turned dark. Bill flipped up his hoodie and began to rush home. Looking up at a particulary powerful lightning bolt, he noticed something unusual about one of the office buildings a few blocks away -- one of the lights in a window turned out, while another next to it turned on. The rain began to subside, and Bill, desperate to find someone he could work with to figure out what was going on, headed over to the office complex.
Now, in this story, I've used a lot of different elements, and they all imply something. The car accident and bag of groceries imply something happened suddenly. The piles of clothes indicate only the biological bodies of the people have disappeared. The rat shows that other living things are still around. The shadowy figure in the hospital, the disappearing red minivan, and the lights in the office building seem to indicate the player may NOT be alone (even if, in the course of the game, they never actually find anyone). There are some elements of things moving on their own, such as the hydrant spray, the newspapers, the falling mop/display, the rat, the lights in the office, the weather. These would depend on your engine's ability for cutscenes or timed events, other than just free exploration of a static scene.
I'm not saying you have to use ANY of these. But deconstructing this story will really help with setting up the environment. If I know I can have moving props (a shelf that crashes over, lights that flicker out when you pass, whatever) I can design the world differently. Simply having an empty, still world with no interaction and no indication any activity had EVER taken place (as if the world is some sort of reconstructed simulation for the protagonist only) can be scary in itself.
Think of this less as a PLOT, and more of a framework. Knowing what ideas you have in mind (or what ideas you definitely do NOT want in the game -- like the piles of clothes) will help -- many of these elements may imply something you want to avoid (like some kind of religious rapture, or the idea that there is someone else is there). Maybe this is a dream, maybe it's real. Maybe all the others have been taken, maybe only YOU have been taken and this is all some elaborate "cage" for you to inhabit. It doesn't really matter at this point, apart from what elements can or can't be used in constructing the world model. And again, I don't know what your engine is capable of doing, other than displaying the model, movement and camera view, collision, and gravity.
Clarifying these points (for the designers, not necessarily the players) will make the final result stronger.