If I steal car model X, fully tune it and then trash it, will those mods still be applied to the next X that I steal? Or will X be a stock setup?
I'm not sure if I understand the question correctly.
But, from my understanding, No. Once you steal car X and tune it, it becomes a unique car, if car X gets destroyed and you can't repair it then you have to steal car X again and tune it again.
The only exception you have is for character specific cars. Like Trevor's Jeep, Michael's Audi and Franklin's Dodge/Ford. If you apply upgrades to them cars and then you destroy them, they will re-spawn with the upgrades there.
So answering directly to the question: It will be stock setup.