Bumper covers are basically pretty things that hide the hole around
the the bumper(impact bar) so it can move and not damage the vehicle
excessively at low speeds.  They are part of an "assembly" that
attaches to the sheet metal on the outside edges and "energy absorbers
in the middle__under the car.  Parts or the "assembly" are usually
constructed from Aluminium and various types of plastic.  These
materials tend not to rust.  Look under the car and you should see
weep holes to allow splash water to drain.  Rust is not your
problem---The bumber cover is usually held in place over urethane
plastic impact strips or logs if you will.  These strips act as
softeners and form return devices after a low speed collision.  Around
the edge of the bumper cover-in the center section of the
assemby--LOOK UNDER the car again, plastic interference fit type
fasteners--they look like fat nails with fins--hold the cover to the
actual bumper.  If the cover has a section that is sagging, then some
of these "finned fasteners," usually called "plastic rivets" are out
of place, or the supporting urethane strip is in need of attenion.
This condition could be indicative of an improper repair.  Removal and
replacement of the rear bumper assembly is usually not an all day
project.  With luck, you will find two or three bolts or nuts on each
end--where the plastic meets the quarter-panel.  Then, underneath ,
two to four bolts per attachment to the energy absorbers.  It helps to
have sockets and wrenches of 10, 11, 12 13, 14, and 17 millimetersizes
for all the possibilites