Walking with only one shoe, if the other one is damaged is prohibited in Islam
If someone walking with shoes on, and breaks or tears one of them, he should not walk with only one shoe, while his other foot is bare. He should either repair the broken shoe and wear both, or take off both and walk barefoot. Walking barefoot at times is sunnah. The evidence for this is the narration of Abu Hurayrah that: “The Prophet (peace and blessings of Allaah be upon him) said: ‘One should not walk with only one shoe. One should either wear both or take both of them off.’” (Saheeh al-Bukhaari, no. 5518)
The scholars have said a number of things about the reason for doing so. The most authentic of these is what has been described by Ibn al-‘Arabi and others that “It is the way of walking of the Shaytaan”.(Fath al-Baari, 10/310) The evidence for this is the report of Abu Hurayrah (may Allah be pleased with him): “The Prophet (peace and blessings of Allaah be upon him) said: ‘Indeed the Shaytaan walks in one shoe.’” (al-Silsilah al-Saheehah, no. 348)
May Allah guide us through the right path