The Halacha requires that all of the Sisit strings passing through the hole of the Tallit remain entirely intact. If even one string at this critical point becomes ripped, the Tallit is invalid and the Sisit of that corner must be retied. Generally, one can rely on the Hazakah (status quo) that the strings are intact. However, it is advisable to occasionally check the strings in the hole.
The Be’ur Halacha (Rav Yisrael Meir Kagan of Radin, 1839-1933), in Siman 12 discusses a case in which the string became ripped in the G'dil-the knotted part of the tassel. This could happen if one of the strings became plucked and clipped on an object. The Halacha states that if two or more strings were severed, the Tallit is invalid. If only one string was severed, it must be torn below the first knot, at least "Kdeh Aniva"-1.57 inches in order to be valid.
A string of Sisit torn in the hole of the Tallit invalidates the Tallit.
If the string was severed in the knotted section, it is valid, if two conditions are met:
1. Only one string was torn
2. The tear occurred at least 1.57 inches below the first knot.