Snakes can sometimes try to eat their own tails, a behavior known as the ouroboros. However, a snake cannot completely eat itself, and it will not disappear or double in size. Instead, it will take up roughly the same volume of space and weigh the same, but it will change in shape to a tighter and tighter hoop as it eats more and the tail begins to be inside several layers of its stomach, making the hoop thicker in diameter (possibly as much as double or more the original diameter). At some point, to continue eating, the snake will have to break its neck at the joint connecting to the skull to take the last possible bite, which would kill it. The digestion would continue for a while until decomposition takes over, at which point the snake would finally begin to "disappear".
The behavior of a snake eating itself is rare, but it can happen due to stress, temperature regulation issues, hypermetabolism, hunger, shedding, constrictive habitat, illness, or confusion. If a snake begins to self-cannibalize, reducing the temperature by turning off heat lamps and spritzing the snake with cool water can help alleviate the stress, and the snake may let go, though sometimes intervention by a veterinarian is required. These episodes can be fatal, and snakes can suffer from blood loss, infection, and suffocation if they continue to devour themselves.