Question:
My tzizis have two corners that have lost a string, each one still has a very small part of it attached, are they still kosher?
Answer:
If the string that ripped is after the knots, and it is only one string that ripped on each corner, the tzitzis are kosher. However if the string that ripped is at the part that connects the tzitzis to the garment then they are posul.
Sources:
Shulchan Aruch O:CH 12-1,3.