Fusing string is a very helpful technique to know when doing blind repairs and can be also used for other projects that use polyester sting. This technique does not work on cotton string, or other non-synthetic string.
First, place the 2 ends together as shown:
Second, with a lighter, burn the 2 ends until they start to melt:
Finally, roll the melted ends of the 2 strings together:
Be careful as the melted string will be hot, so do the last step fast. You might even want to wet your fingers before the last step.