Talmud for Shabbat 223:10
והוינן בה [ר' יוחנן] אליבא דמאן אילימא אליבא דרבנן מדלענין טומאה מנא הוי לענין שבת נמי מנא הוי אבל לא לחליצה דלאו מנא הוא והתנן חלצה של שמאל בימין חליצתה כשרה ואלא אליבא דרבי יהודה מדלענין טומאה לאו מנא הוא לענין שבת נמי לאו מנא הוא אבל לא לחליצה דמנא הוא
or its two strappings are broken, or if the entire sole is removed, it is clean.<span class="x" onmousemove="('comment',' For here too it ceases to be a 'utensil'. ');"><sup>24</sup></span> If one of its ears or strappings [is broken], or if the greater part of the sole is removed, it is unclean. R. Judah said: If the inner one is broken, it is unclean;<span class="x" onmousemove="('comment',' For it is still a 'utensil'. ');"><sup>25</sup></span> if the outer, it is clean. Whereon 'Ulla-others State, Rabbah b. Bar Hanah said in R. Johanan's name: Just as the controversy in respect to uncleanness, so is there a controversy in respect to the Sabbath,<span class="x" onmousemove="('comment',' If it is a utensil in respect of the former, it is likewise so in respect of the latter, and may be handled on the Sabbath. ');"><sup>26</sup></span>
Jerusalem Talmud Shabbat
Ritual impurity biblically is restricted to Jewish persons, food, vessels and tools, and a leprous house. If a vessel or tool was damaged beyond repair, it becomes ritually pure. As usual, impure means “a possible candidate for impurity” and pure “unable to become impure.” Rebbi Jehudah holds that people will repair even serious damage to their shoes if it can be done so as not to be noticed in public. The rabbis hold that even in such cases, people will not repair severely damaged shoes.
R. Jehudah holds that a person will repair sandals when the repair is not immediately visible from the outside. Therefore, if a strap or hole for the shoelaces is torn at the instep, towards the other foot, the shoe remains usable. The majority holds that one torn strap or a partially torn sole can always be repaired. Rebbi Jacob bar Aḥa, Rebbi Tevele, Ḥanin bar Abba in the name of Rav: Practice follows Rebbi Jehuda as far as the Sabbath is concerned104The same statement in Babli, Šabbat 112b..