Is one permitted to wear shoes without a back (slippers) on Shabbos/ Yom Kippur, or is it considered carrying since they are likely to fall off when walking in the street?
This is a good question. There are poskim that say not to go outside wearing slippers that don’t have a back to them, because they may fall off and the person may carry them in the street. This would be true to most slippers without a back, and especially with “filp-flops” that don’t even have sides to them and are only held to the foot by a piece of plastic between the toes. However many other poskim say that although this is true, nowadays that people don’t walk outside at all without slippers etc. there is no fear that one might continue walking, and therefore all types are permitted, on Shabbos and on Yom Kippur.
Rema O”CH 301- 16, M”B ibid, Rivvos Ephrayim 4-97-11, Oz Nidberu 5-35, Orchos Shabbos 28- 126, Yisodei Yishurun 39 Melachos 2- pg. 215, Orh L’tzion vol. 2- 23-4.