The donor cars are usually unuseable in their current state because of decaying body panels, regardless of whether or not their running gear is fine. Westfield says it recycles as much of the MX-5 as possible into the new car, a claim substantiated by the wheels on the car that come straight off of the original.
The idea of recycling a car yourself rather than placing that burden on automakers could catch on if hot, little two-seat British sports cars are the end result. Due to the Miata's popularity with autocrossers and the success of the Spec Miata racing series, however, we doubt many of these iconic roadsters ever end up on the scrap heap.
[Source: Westfield Sportscars via Piston Heads