I've had the problem on one of my instruments, and found that I could salvage a "ball" from another string, slip it into the loop, and with only moderate dexterity get it to work quite nicely. You may have to hold it together until you get a little tension on the string.

This may not work with all kinds of balls, and you can't do it if you don't have the balls for it, but...

(leaving quietly)

John