Unfortunately, the terms "destroyed" and "repairable" are not defined anywhere in the regulations. But, as you might expect, the FAA has a policy/opinion about what these terms mean. In fact, the FAA has issued Order 8100.19, Destroyed and Scrapped Aircraft which spells out what these terms mean and how they are to be applied by FAA inspectors. If an aircraft is capable of being repaired and returned to service after it was unserviceable due to wear and tear, damage, or corrosion then it is "repairable." But this means that when the repair is complete the aircraft to returned to service in "its original (or properly altered) condition that conforms to its type design."
The FAA clarifies further that an aircraft is only eligible for repair if it has at least one primary structure around which a repair can be performed. According to the FAA, it "considers an aircraft’s primary structure to be the structure that carries flight, ground, or pressurization loads, and whose failure would reduce the structural integrity of the aircraft." If only some, but not all, of the major structures of an aircraft are replaced, then that would still be considered a repair.
However, if all of an aircraft's primary structures must be replaced then the FAA does not consider the aircraft to be "repairable." Rather, in that situation the aircraft is being "replaced" after being "destroyed." And if the identification plate from the original aircraft was then placed on the "destroyed" aircraft that would violate 14 CFR § 45.13(e) ("No person may install an identification plate removed in accordance with paragraph (d)(2) of this section on any aircraft, aircraft engine, propeller, propeller blade, or propeller hub other than the one from which it was removed.”)
In order to comply with Section 45.13(e), the primary structure must be identifiable and traceable to the particular aircraft and its identification plate. As an example, if a heavily damaged aircraft is repaired by performing many major repairs on its fuselage and replacing all other primary structures that may be destroyed such as the wings and the empennage, that aircraft would not be considered destroyed because the fuselage is repairable. But if the fuselage of that aircraft also needed to be replaced along with the other primary structures, then the aircraft would be considered destroyed.
The Order also provides the following examples for use in determining if an aircraft is destroyed:
All primary structures of an airplane or glider, including the fuselage, all wings, and empennage are beyond repair.
The fuselage and tail boom of a rotorcraft are beyond repair.
Only the aircraft identification plate is reusable.
How is this determination made by FAA inspectors? Well, according to the Order, "FAA accident investigators will apply their specialized knowledge and expertise and follow the guidelines in this order when evaluating aircraft wreckage to determine whether an aircraft is repairable or should be declared destroyed."
Fortunately an aircraft owner can dispute a determination that an aircraft is destroyed by providing the appropriate FAA FSDO or ACO with a repair process that explains how the damaged aircraft can be repaired provided that at least one primary structure of the aircraft is capable of being repaired rather than requiring replacement. If you are faced with a situation where it is unclear whether an aircraft has been "destroyed" or is still "repairable", you will definitely want to consult the Order, as well as the aircaft's maintenance manual.