One of my players has a 7th level druid who has the cave domain. The cave domain grants Tremorsense (Ex) 30 when 6th level is reached. What I'm trying to figure out is what happens to this sense when they wild shape. Does it get treated as if it belonged to the form, like when a race has darkvision, and thus is lost while wildshaped, or does it somehow bypass the form changing and remain active?
Your player would keep Tremorsense
The Polymorph subschool says:
While under the effects of a polymorph spell, you lose all extraordinary and supernatural abilities that depend on your original form (such as keen senses, scent, and darkvision), as well as any natural attacks and movement types possessed by your original form. You also lose any class features that depend upon form, but those that allow you to add features (such as sorcerers that can grow claws) still function.
The Cave Domain granted power says nothing about being restricted to only certain races, which very strongly suggests that the granted power is not dependent on original form. Thus, it seems to qualify as a "class feature not dependent upon form", and would be retained by the Wild Shaping Druid.