There's definitely potential ways for PD to stop them from existing. The most straight-forward that I can think of is a more thorough check system being put in place. As a simple example: say someone has swapped a Viper engine into the Ram. The game would check the value for the car's engine when you get in the vehicle, and would compare that value against the stock one. If it's anything other than the normal value, well, PD could program whatever sort of response they want. Maybe the game wouldn't let you enter the car, and would give an error message. Maybe it'd give a different error message and erase the car from the garage.
The check would extend to all parts, such as tires, and the chassis itself, only allowing the parts that are typically available to the car within a normal play-through. It could also extend to settings, to ensure nobody has given themselves too much downforce, different gear ratios, or the like.
As the check would be on the game-side of things, and not anywhere involving the player's save, modifying saves would then accomplish nothing. The check could also be done at any point in the game; heck, if PD wanted to, a message could pop up as soon as you load up the game, informing you it's checking your entire garage for "erroneous cars".