This glitch is only easily possible in multiplayer, but it can happen in Campaign as an Elite or a Spartan, although this only happens to Spartans in Multiplayer. It causes the neck to stretch, or sometimes makes limbs and the waist stretch.
To do an example of this, go onto the map Midship, and find one of the Stationary Shield Generator. Crouch down and keep walking towards the shield, so you don't bounce away. Get somebody to assassinate you. If you do this right, the Spartan's head should go through the shield with the body on the other side. The shield makes the body pull away, but it can't because the head stops it from doing so. This causes the Spartan's neck to stretch like a rubber band. Sometimes it flops around wildy.
Also in Halo 3, when a player dies and hits something violently (or, on occasion, is hit by something violently), there is a possibility that they will stretch, but it only happens for a split second. Sometimes AI Marines and rarely Brutes stretch.