Was Julia a double agent for the Thought Police?
Her reaction to Winston reading the book by Goldstein is complete disinterest, as is any thoughts he has on politics - although BB wanted a society that was utterly disinterested in politics.
But I think Winston would have not moved past his diary to actually threatening BB without Julia; she gave him enough rope to hang himself with, encouraged him with her dissent to behave with more dissent himself. O'Brien mentions he's being watching Winston for years - maybe BB decided to act against him by sending in Julia as his catalyst.
There's no mention of what BB did to Julia in Room 101, or how they tortured her - maybe they gave her the scar for good colour. There's no mention of even her last name.