I just spent all of 5 hours trying to fix a Lada. This required many trips back and forth between industrial areas.

Whenever I added a new wheel and left the area, it would move itself downhill 50-200m from wherever I saw it last. This happened three separate times, each time I added a new wheel, and the Lada would move further away from Pusta downhill until it was next door to the North Elektro firestation.

SOLUTION: (note, I've tried this solution once, but it worked) If you get into the broken Lada, you can still switch gears using [Q] and [E] keys; the solution is to switch the gear of the Broken Lada into Neutral. You will know it's in neutral if you hit Q until you hear no more shifting (this means you're in Reverse), then hit E one time. This put the Lada in neutral, and when I left it there and came back, it was in the same spot I left it.