Is every shape possible with a snake?
Solution 1:
If you will forgive a bit of Unicode box art, I think this is a counterexample:
┌──────────────────┐
│ ┌─────────────── │
│ │ ───────────────┘
│ └────────────────┐
└──────────────────┘
The horizontal lines are supposed to be 1 apart. It has to be sufficiently wide for the example to work.
Edit: A bit of explanation may be in order. The recipe for snake folding is reversible, so if this snake is reachable, it can be unfolded into a straight line. But there is no legal move from this configuration.