i think your question involves two different concepts: 1. illegally transferring a VIN number and 2. "rebodying" a "restored" car.
"removing a VIN" is pretty easy to understand - you have physically removed the VIN number on one car and physically attached it to another car. THAT is illegal. period. but what about your second question - how much of a car can you "replace" and still have the "original" car? my understanding is that replacing over 50% of an original car makes that car a "rebodied" car. a "rebodied" car IS NOT "illegal" so long as the original VIN number on some part of that car remained on that car. HOWEVER, you DO have to disclose these repairs if you sell a "rebodied" car or you may be in for a civil lawsuit.
look at what plymouth did on the a body barracudas 67-69. on those cars, the "VIN" or "order number" was stamped on the radiator support (front of car), the same official number was placed on the dash or drivers door pillar (middle of car) and the same official numbers were stamped on the driver's side trunk water channel under the weather stripping (rear of car). for these cars, for a front end collision, you could "legally" cut out the original stamped number on the radiator support and put that number on the "replacement" "repair" part. that would be legal. the same process could be done for the dash and rear trunk water channel numbers.
now suppose you had a 69 barracuda that was hit hard in the front and back. if you replaced the entire "front clip" and then put two new rear quarters, deck lid, lower valance and a few other misc. panels, you would probably have replaced more than 50% of the car. assuming you replaced the official numbers on the new parts, you would have a "rebodied" car. in the collector car market, rebodied cars are NOT worth as much as cars that are ALL original or that have only a few body parts replaced. that is why not disclosing all the repairs to a vehicle when you sell it opens the seller up to a civil lawsuit.
so again, two concepts: an "illegal" car with a replaced VIN number OR a "legal" car with its original VIN but still being a "rebodied" car.