No crush protection, just abrasion. If you need crush protection there is wiring channel protection that can be placed over the cable to withstand foot or even vehicular traffic. Though I would consider the situation before putting any cable run in a common area with foot traffic.
For this particular case I'd look into getting a aluminum door threshold. They are usually extruded aluminum and have tall ridges with hollows on the back side. If you could find one with the right amount of clearance on the bottom it protect the wire and wouldn't cause a tripping hazard or look out of place.