The Halacha mandates that each of the four corners of the Tallit have Sisit comprised of eight strings each, totaling 32 strings on the Tallit. However, it is not uncommon for strings to tear or become detached. The Poskim discuss at length in which cases the Tallit remains kosher even though its strings are incomplete. Nevertheless, The Kaf HaHaim (Rav Yaakob Haim Sofer, Baghdad-Israel, 1870-1939) emphasizes that even in cases in which the Tallit is still kosher, that only means that one does not have to remove it immediately, and if he has no other, he may continue to use it. However, as soon as possible, he should fix the Sisit so that there are 32 complete strings.
Maran brings down a dispute between the Rambam and Rabbenu Tam as to how many strings may rip without invalidating the Tallit. He brings the Rambam as the "Stam" (unattributed opinion) and Rabbenu Tam as the "Yesh Omrim" (minority opinion). The Rambam holds that, assuming one is careful to keep the same four strings on either side, all a Tallit needs is four strings on one side of the Sisit to be "K'deh Aniva" (minimum length to wrap a loop, equivalent to 1.56 inches), and the other side can be totally clipped. Rabbenu Tam, based on his understanding of the Gemara in Menahot, holds that each Sisit must always have two complete strings. The other strings can be reduced to "K'deh Aniva." Therefore, if one or two strings were ripped off, the Sisit is still kosher because two other strings certainly remain fully intact. However, if three strings were ripped, the Tallit is invalid because, there are no longer two full strings remaining intact. Maran concludes that one should follow Rabbenu Tam's opinion.
If Sisit strings become ripped, one must first verify that the Sisit were made according to the custom of keeping four strings separate on either side. If so, then if more than two strings become ripped from the Sisit, the Tallit is no longer kosher. If two or less strings become ripped, the Tallit is still kosher, but every effort should be made to repair the strings, as soon as possible.