If Tzitzit found to be not kosher on Shabbat

p. 36 Chapter Thirteen The Laws Concerning Zizit on Shabbat

3. If one discovered on Shabbat that the tallit one is wearing is halachically not in order and one is in a karmelit, (a place where the prohibition of carrying is of Rabbinic degree) one does not remove it before returning home, as in this case consideration for human respect outweighs the halachic problem. (Sh.Ar.ibid)  Even the tallit kattan which is worn underneath the clothes does not have to be removed as it is degrading for a person to have to take off his clothes.  Similarly, if someone in synagogue finds that one of his zizit is broken off and he is embarrassed to be there without a tallit, he may put on his tallit without saying the blessing, because of the importance attached to human respect; this, however, only applies on Shabbat when it is forbidden to make ziziot - on weekdays this is forbidden. (Rema, ibid.)  If he knew already before Shabbat that it was halachically unfit, then he may not put on that tallit on Shabbat, because he should have repaired it before Shabbat; however, if there are no ziziot available in town, the same ruling applies as if the broken ziziot were discovered on Shabbat (Magen Avraham, ibid.)

Note from us: Please consult your own rabbi to find out what to do - these are for learning purposes only.
As quoted from:
Shulchan HaMelech, a Kitzur Shulchan Aruch in 3 volumes as compiled by Maharan HaRav Shmuel Laniado z'al, 1923 with the supplement "Al HaShulchan" containing various opinions compiled by Ezra Basri, Chief Justice of the District Court, Jerusalem in 1992.

We would like to dedicate this learning for the speedy and complete recovery of two people: our friends' 5-year-old son, Joseph Benjamin, son of Ireneusz Khrystof, diagnosed in April with ALL leukemia, and a longtime friend of the family, Franco, son of Joseph, who is B"H recovering from thyroid surgery. Please have them in mind when studying. If you would like updates on their progress, please let me know so I can tell you when I find out from either or both.

 B"H we did our second Happiness Conference Call Tuesday night on skype, reading the Rabbi Pliskin Happiness book as a merit for these and other cholim - we thank those who participated and hope you will all join us for the next installment tonight (Thursday) at 9pm (contact me to find out how to join - aimee.cohen@gmail.com)