The phrase "soft rubber" refers to a type of material that is flexible and not too hard. It can be easily bent or squeezed and is often used for making items like erasers, pencil grips, or protective coverings. Full definition
The damage to the tread is consistent with your description of rough roads especially if that is combined with softer rubber compounds. (mechanics.stackexchange.com)
These cubes are made of soft rubber, have rounded corners and washable covers. (michigananimalhospital.com)
Each pen has a wide, soft rubber grip that's color coordinated and makes them super comfy to write with. (geekwrapped.com)