If you do not have active Camo and you exit the game, your island is vulnerable to attack from other players! The attacking player will be able to steal some of your supplies, but never all of them.
You can protect your island with defenses and fortify it with walls and mines. Placing terrain at the edge of the map does not stop attacking units.
If you have any further questions about this or Battle Islands in general, please go to this page and fill out the game questionnaire!