46. Disposing of Tzitzis Strings
9:19 Tzitzis that break or that are removed from their garment should not just be thrown in the trash since doing so would be disrespectful to the mitzvah. Some people use old tzitzis strings as a bookmark in sefarim; since they were once used for a mitzvah, it’s appropriate to use them to assist in Torah study, which is also a mitzvah. Similarly, one should not use the discarded garment for any disgraceful purpose (such as tearing it up for rags). Apparently, one may dispose of the worn-out garment in the trash. (See Mishnah Brurah 21:13.)
9:20 Let’s suppose that, upon arrival at shul on Shabbos, a person discovers that one of the tzitzis in his tallis has become invalid and that he is unable to locate a fit tallis to wear. (And, being Shabbos, he is unable to repair his own tallis.) If he is embarrassed to sit there without a tallis, he may wear his tallis but he may not recite a blessing over it. This is only the case where he did not know before Shabbos that the tzitzis had become invalid; if he knew about it before Shabbos and failed to repair it, he may not wear the invalid tallis. (If he knew but forgot, there is room to be lenient – see Mishnah Brurah 13:13.)