As Nenneth said, when you loose the aglets of your shoelaces, it becomes very difficult to weave them through the eyelets. Here's what I do when that happenes:

I usually use a lighter to burn the open, untwisted ends of the laces, and pinch-roll them into tight little 'sausages' with wet index finger and thumb.

Yes, this even works with cotton laces. They usually contain a small ammount of synthetics..... and even if not, the charred cotton gives it quite a good hold so you can get the lace through those holes again. :)