In almost every case, department stores at malls are not paying rent. They built, and own their buildings, and often the parking lots closest to their stores. It actually is a big pain in the butt for mall owners, because the department stores have veto power over new construction at the mall that might have an impact on the department stores, even when the impact is minimal. We're going through that at the mall near me, where there are actually four different owners, Sears, JC Penney, Federated, and Evershine (mall owner), and everything the mall owner wants to do is subject to approval by the department store owners.
The department stores really can't do anything else with their mall stores except to continue to operate them, or try to sell them to another departments store chain. The zoning is such that they can't just run out and tear down the store and build condos.