The Death by Cryo Tube is a collision-related phenomenon in Halo: Combat Evolved that causes players to be pushed through the ground, where they inevitably fall to their deaths.
Just after the first cutscene in the Pillar of Autumn, you begin thawing from a cryo tube. Right after you jump out of the "hushed casket," jump on top of the tube, so that you are under the cryo tube's cover. When the cover closes, you will be pushed "through the ground" and "fall to your death."
Sometimes the cover will not push you through, but instead will close and trap you in the cryo tube; this is especially common if you crouch before it closes. If you turn away from the cover, you can see a headless Master Chief laying in the tube, and if you look down, you can see what appear to be clones of John-117 for a few seconds. You can do this by jumping on the tube and crouching before it closes. Sometimes the cryo tube will instead push you through parts of the level.