If a person comes to the synagogue and discovers that his Talit is Pesula (invalid for use), and no valid Tallitot are available, may he wear his Talit Pesula to avoid the humiliation he will experience participating in the service without a Talit?
The Mishna Berura discusses this issue in Siman 13, and rules that on Shabbat, one may, indeed, wear a Talit Pesula to avoid embarrassment. (No Beracha would be made when donning a Talit Pesula.) The reason behind this Halacha involves the precise nature and definition of the Mitzva of Tzitzit. The Torah does not directly prohibit wearing a four-cornered garment without Tzitzit; rather, it obligates one to affix Tzitzit to a four-cornered garment that he wears. Now on Shabbat, one cannot affix Tzitzit to his garment, due to the prohibition against tying knots on Shabbat. Strictly speaking, then, one transgresses no violation by wearing a four-cornered garment on Shabbat without Tzitzit. Since the law of Tzitzit does not prohibit wearing a four-cornered garment without Tzitzit, but rather obligates one to affix Tzitzit to such a garment, in situations where this is impossible one may wear a four-cornered garment without Tzitzit. Therefore, for purposes of avoiding humiliation, Halacha would allow one to wear a Talit without proper Tzitzit on Shabbat. If one will not feel ashamed sitting in the synagogue without a Talit, then this leniency does not apply, and he may not wear a Talit Pesula.
During the week, however, when one is obviously permitted to tie Tzitzit to a garment, this reasoning does not apply. Since one bears a Torah obligation to affix proper Tzitzit to his four-cornered garment, Halacha forbids wearing an invalid Talit on a weekday, even in the face of humiliation. Although Halacha places very strong emphasis on the value of Kevod Ha'beriyot – human dignity, this value does not override Torah law. Therefore, just as a person who realizes he is wearing Sha'atnez (a garment woven from wool and linen, which the Torah forbids to wear) must immediately remove the garment even in public, so is it forbidden to wear a four-cornered garment without proper Tzitzit even if he will suffer embarrassment as a result.
Incidentally, this Halacha results in a very unique phenomenon: an action that is forbidden during the week, but permitted on Shabbat.
Conclusion: If one has no access to a valid Talit and will suffer humiliation sitting in the synagogue without a Talit, then on Shabbat he may wear a Talit Pesula (without Beracha), whereas during the week he may not.
