Sayyiduna Ali (may Allah be pleased with him) narrates: If the strap of one of the Prophet's (peace and blessings be upon him) sandals broke, he would walk wearing one sandal while the other was in his hand, until he found a strap.
Imam al-Tabarani recorded it in al-Mu'jam al-Awsat, and its chain is hasan (good).
Hadith Referenceمجمع الزوائد ومنبع الفوائد / كتاب اللباس / 8633