I noticed that a single string of my Tzitzis tore from the area of the knots. The torn string is coming out between the first and second top set of knots and I assume that it originally tore above the double knot and somehow unraveled to now be between the first and second knot. Is my Tzitzis still valid?

Answer:

According to the rulings of Admur in his Siddur, which is the final ruling followed by all Chabad Hasiddim, you should immediately remove the Tzitzis and redo that corner with proper strings unless you know for certain, as you are assuming, that the tear occurred above the double knot and then later unraveled.

Explanation: According to the rulings of Admur in his Siddur, which is the final ruling followed by all Chabad Hasiddim, if even a single string tore within the area below the loose strings, meaning within the braided area, the Tzitzis is invalid, and that corner must have its Tzitzis redone. The reason for this is because we view it as if that entire string has now torn on both sides and therefore it is as if that the Tzitzis has only three whole strings and not four as is required. According to the simple understanding of this ruling of Admur, this would apply even if the string tore within the top double knot area, and therefore in a case of doubt such as you are describing in which you do not know if it actually tore there, or tore above the knots and only later unraveled, I would apply the rule of Safek Lechumra, just as we apply regarding other cases of torn strings, such as a string tore from each side in which case we invalidate the Tzitzis even though we don’t know for certain that they are from the same string and indeed invalid, nonetheless since it is still a doubt we are stringent and I would apply the same here according to our stringent ruling of Admur in his Siddur. However, if it were to be determined for certain that the string had torn from above the double knot and simply later unraveled, then my understanding is that it would remain permitted even according to the novel ruling of Admur in his Siddur, as certainly he does not hold that if the double knot loosened and some of the strings came out of the double knot that the Tzitzis becomes invalid, and the main invalidation is only when the tear occurred within that area to begin with. To note, that all this is only according to the rulings of Admur in his Siddur and the Poskim that his ruling is based on, however according to the vast majority of Poskim, including Admur’s own ruling in his Shulchan Aruch, the Tzitzis would remain valid even if it tore within the braid and the double knot area. Nonetheless, even according to this technical validation according to these Poskim, it is always an act of piety to have a full eight string Tzitzis and therefore bottom line everyone should always redo the corner with new strings if even a single string has tore, although according to Admur in his Siddur if it tore within the braid or double knot it would be an actual obligation and it is forbidden to continue wearing the Tzitzis until it is fixed.

Sources: See Siddur Admur; Shlah Chulin 112a in interpretation of Rav in Menachos 39a; Elya Raba 8:10 in name of Taz and Shlah; Emek Haberacha 2:13; Soles Belula 12:2; Regarding the dissenting opinion see: Admur 12:6; Biur Halacha 12:1 “Yeish Lismoch”; Kitzur SHU”A 9:13; Tehila Ledavid 12:2 See regarding Midas Chassidus to always redo the strings even if only one string Torah and remains valid: Chesed Lealafim 12:1; Ashel Avraham Butchach 12 in name of Rav Menachem Mendel of Rimnov; Rebbe Rayatz in Sefer Hasichos 1944:56; Rebbe in Igros Kodesh 13:29 [printed in Shulchan Menachem 1:41]; See Admur 15:5 that implies such a Chumra does exist; Makor Chaim 12:15; Sfas Emes Shabbos 118b; Kaf Hachaim 12:12; Shulchan Hatahor 15:1; Piskeiy Teshuvos 12 footnote 2