תלמוד על שבת 223:11

¹⁰¹This paragraph and the next are also in Yebamot 12:2 (Notes 62–80, א).“A sandal whose holes, edges, or loops¹⁰²Explanation of Arukh, Arabic שראך “loop, net”. are torn or one of whose soles fell off is pure. If one of its holes, edges, or loops is torn or most of its soles fell of it is impure. Rebbi Jehudah says, on the inside it is impure, on the outside it is pure.”¹⁰³Tosephta Kelim Baba Batra 4:5; Babli Šabbat 112a.
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..