Talmud for Menachot 82:15

[Each] zizith is inserted [in a hole] within three finger-[breadths] of [each] corner; farther away than this is invalid If it was inserted in the border, it is invalid; if between a handbreadth [from the edge] and the border, it is valid. R. Eliezer b. Jacob declares it to be invalid. [If a strip less than three finger-breadths in length]¹⁷So according to Men. 41a (Sonc. ed., pp. 247f.). was cut off [from a ṭallith]¹⁸That had no zizith (Rashi ad loc.). and then rejoined to it, [the ṭallith] is valid. R. Meir declares it to be invalid.¹⁹His reason being that, as it is proper to insert zizith within three finger-breadths from the corner, one might use a hanging thread left from the sewing as one of the four threads required for the zizith. But that would render the entire fringe invalid, since all the threads have to be made specifically for the purpose of the commandment, whereas the hanging thread was one ready made (cf. Men. Sonc. ed., p. 248, nn. 1f.). [If the detached part] was made into [a smaller ṭallith] on its own, it is valid.