For onboard employees, there are strict definitions for suitable shoe. They must be leather (I.E., not fabric); they must have a solid, enclosed toe; they must have something that secures them on the foot (laces, straps & buckles; Velcro; etc.), and they must have a definite heel, rather than having a flat bottom surface. However, in my 20+ years with Amtrak, I have never heard a definition of passengers' shoes. It has always been understood that bare feet or socks alone are not shoes, and we have always told passengers gently but firmly that they would have to wear shoes whenever they are away from their seats or sleeper accommodations. We wince when we see sandals, flip-flops, or soft shoes, but we can't really tell the passenger that he or she is violating a rule. I would try to gently suggest they be careful & hope they get the message.