The first things I do when I by a new pair of Tracksters, is cut the stirrups off and tie the ends of the drawstring together (you can still tie them when you've done this). There was a time when Tracksters came with one of those tie clasp things on the string that can be found on rucksacks and stuff. It's probably possible to buy these tie clasps at outdoor/climbing retailers to prevent accidental drawstring loss.
To get the string back in, you can attach a large safety pin to one end and simply thread it back through. It's a bit fiddly, but it works. :d