Prison!

Although that small cloth seemed useless,with critical thinking, one would be able to find several suspicious points. What was a bandana used for? Obviously to wrap the head. For the exceptionally charming Jack Sparrow, it was used as an alluring aesthetic. Most pirates used it for warmth and to shield against the rain. There were no corpses near the spot where the bandana was discovered , that meant that this should have been placed down by the owner on purpose. Looking at the torn and jagged side of this cloth, it should have been ripped apart instead of being sliced off from a sharp weapon. Therefore, what would a pirate tear apart his bandana underneath a random tree be thinking? The bandana was a cloth that was the least likely to be dirtied, therefore, it was obvious that the most logical explanation was that it was used to wrap a wound!