Annoying, you make a beautiful bag with a drawstring, that cotton cord starts to unravel at the end. Shrink plastic to the rescue!
Cut a piece of this plastic tube to size, slide it over the end of the cord and hold a flame for a moment. The plastic shrinks nicely around the cord and you're done. Also very suitable for hoodies, because the plastic can be washed in the washing machine.
Price is per 50cm.