Transponders began life as military IFF, Identification, Friend or Foe, as most of you know. It was silent until interrogated by a ground based secondary radar, or IFF interrogator. The transponder receives on 1030 MHz and transmits on 1090, just the opposite of the IFF interrogator.
Mode A was the original, a 4 digit code. Mode C, altitude, was added to the reply later.
Mode S supplements the A and C replies, and was developed in the mid-1980s to provide extended info such as tail number to ground based interrogators, and to open the path for TCAS II. In fact, ground based interrogators fell years behind TCAS in deployment.
The TCAS II device is similar to a ground based interrogator: it transmits on 1030, and receives on 1090. It can receive replies from any IFF or transponder, but can only coordinate avoidance maneuvers with another TCAS II and Mode S equipped aircraft.
Coordination is dictated by the plane with the lowest tail number. The tail number, or aircraft Identification code is wired into the airplane. It's bizarre, but a Mode S transponder without its tail number will be blind to other aircraft, and its own TCAS will be inoperative. That's one more variable for the investigators of the Brasil midair.
Back to the original question: I can't imagine why ATC would be asking for a code change on final approach. Did they screw up and assign the same code to two different a/c?
GB