Talmud for Shabbat 223:9
מאי היא דתניא סנדל שנפסקו שתי אזניו או שתי תרסיותיו או שניטל כל הכף שלו טהור אחת מאזניו או אחת מתרסיותיו או שניטל רוב הכף שלו טמא ר' יהודה אומר נפסקה פנימית טמא החיצונה טהור ואמר עולא ואיתימא רבה בר בר חנה אמר ר' יוחנן כמחלוקת לענין טומאה כך מחלוקת לענין שבת אבל לא לענין חליצה
seeing that I could change it from the right [foot] to the left?<span class="x" onmousemove="('comment',' A sandal had two strappings, perhaps like loops, through which the laces were inserted, one on the outside and the other on the inside of the foot. Now, if the inner one is broken, it can be mended, and though it is not very seemly to walk in sandals with the strappings or laces merely knotted together, nevertheless it does not matter, as it is not very noticeable on the inner part of the foot. But if the outer one is broken, one would not walk out in it until a new one is inserted; consequently it ceases to be a 'utensil', and may not be handled on the Sabbath (cf. p. 125, n. 3). In Abaye's case the outer strap was broken, hence R. Joseph's ruling. But Abaye argued that by changing the sandal to the other foot this would become the inner strapping, hence it should be permitted. Presumably their sandals were not shaped exactly to the foot, and were interchangeable. ');"><sup>21</sup></span> — Said he to him: Since R. Johanan explained [the law] on R. Judah's view, it follows that the <i>halachah</i> is as R. Judah.<span class="x" onmousemove="('comment',' That it ceases to be a 'utensil' if the outer is broken. ');"><sup>22</sup></span> To what does this refer? — For it was taught: If the two ears of the sandal<span class="x" onmousemove="('comment',' At the back, by means of which the sandal is held when it is tied up. ');"><sup>23</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..