The game never said its a limited resource ;(
Hello! The short answer is no. Since the world size is finite, almost every resource is limited (with the exception of those dropped by creatures). You are right that the game basically never says that, since I haven't implemented a tutorial. The loading screens do offer some tips about scarce resources and other things, but they are totally random. There are some inconvenient alternatives to gathering strings and derivatives, though. Common chests (those found in the surface) can contain string and cloth. Also, zombies can drop cloth with a 15% chance. I apologize about that, although it was intended by design that the player would need to take care the finite resources of their world.