Agents frequently use possession to move quickly from one location to another. Though the process only takes a brief time, the Agent is vulnerable to attack during this time. The bluepills have no awareness during the possession, and are often confused when they return to consciousness, sometimes badly injured. However, should the Agent "die" while using a possessed bluepill, the bluepill dies as well.
While never clearly stated, Exile's shells may be possessed bluepills, and the programs must change their shells when they are destroyed. This is seen when the Oracle uses a new body after the Merovingian used kill-codes to her old shell which he acquired in exchange for Sati's exile to the Matrix.