Normally the ends of shoelaces are protected with plastic caps to prevent them from fraying, but they sometimes break and get loose. Once the ends of shoelaces start fraying, it is very hard to put them through the tiny holes of your shoes. This is an easy fix:
Get some glue, the right size of heat shrink tubing and a heat gun (or a lighter)
Put a little amount of glue on your finger and wet the ends of the fraying shoelaces with it.
Cut a suitable length of heat shrink tubing and shove it over the end of the fraying shoelace.