Give it time. There's virtually no reason that middle management won't be outsourced eventually (no direct contact necessary with the skilled employees, no direct contact with the highest levels of management), and then it will climb up and down the ranks slowly ("Hey, if we replaced N, why can't we replace M and O?").
Eventually there will be a stockholder meeting somewhere to discuss how the managers in Beijing need to be replaced with some other managers from Bangalore. Nobody will bat an eyelash. There will be two janitors in the building, but those will be the only onsite employees.
You are what you think.