Are these correct:
1) The car he was driving was stolen when he stopped at a rest area to go to the restroom.
2) The police stopped him because the car he was driving was stolen. He claimed that he'd borrowed it from a friend.
3) Her ring was stolen. It was given to her by her boyfriend who was a burglar.
What a fine collection of specimens you have assembled for us here!
Examples (1) and (2) are of course correct, but "was stolen" is clearly functioning differently in each. In (1), "was stolen" is a passive verb phrase relating to a stealing event, which happened while he was at a rest area.
In (3), "was stolen" is, I would argue, not a passive verb phrase at all but, rather, a linking verb ("was") followed by "stolen" as an adjective. Indeed, we could rephrase the end of the first sentence like this: "he was driving a stolen vehicle."
Example (3) I dislike, perhaps mainly because if her boyfriend stole the ring then it was never his to give away! But you've also used "her ring" in that one, which implies that it was hers. The first sentence of (3) could be revised like this:
- The ring she was wearing was stolen goods.
That construction may be a bit old-fashioned (see this, for example), but I like it.