Not much in the rear to burn. Like Manolito says, check the muffler and exhaust pipes for plastic trash melted to them that is slowly burning away. Could also be a brake dragging. Hot brakes don't smell particularly like burning plastic to me, but they could to some folks. Next time the car is parked someplace flat and has had time to cool off, drive it about a quarter mile without touching the brakes. Let it coast to a stop. Get out and carefully feel the rear wheels (not the tires, the wheels). If one is warm or hot, get the brake looked at. Don't burn yourself, brakes can get REALLY hot.
The third possibility would be the wiring or some electrical device in the back of the car. Normally a fuse will blow before smoke and flames appear, but you can't really count on that.