Can a parked car jump timing after being hit twice by the same vehicle

If it was hit hard enough it can damage cam and or crank sensors causing the computer to think the timing has jumped. But the engine having physically jump timing in this vehicle from a collision is almost impossible unless some foreign object entered the engine itself.

Isn't it totaled ?

If it's a Delorian it can jump time

I'm assuming the vehicle won't start. Most likely the electrical system and/or the fuel pump is damaged from the collisions. File a claim against the other person's insurance, get your money, let them total it, and move on. An 11 year old Chrysler is easily replaced! Jim