Yosef Karo, Translation:Shulchan Aruch — Orach Chaim 13…
“ Paragraph 3 - If, while he is in a Carmelit Area on Shabbat, a person discovers that the Tallit he is wearing is invalid, he should not take it off until he has reached his home, because the respect due to other people is greater. Rema: And even a tallit katan worn under one's clothing does not need to be removed and this is the law if one of the tzitzit has become invalid and one is ashamed to sit without a tallit may wear it without a blessing because of the honor of the public. ”
