I've GIVEN away a car for $0. Granted, it needed some work, but it still ran. Some people even pay to have their car taken (e.g. a junker that needs to be towed away).
Before you argue that $0 for a perfectly functional new car is unreasonable, I would point out that game shows and sweepstakes routinely give away cars for $0. And I have seen people on "buy nothing" type groups occasionally give a (admittedly used) car to people in need.
So $0 for a car is not absurd or unreasonable. Perhaps unusual, but not unreasonable.
Also, in contract law, 'unusual' and 'unreasonable' have a very large overlap in their venn diagram.
If the seller and buyer are related, tax obligations are different because it involves a gift or implied compensation, but that's not what we're talking about here.
So it is indeed possible to pay no more than $1 for a car. As for registering the title in your name, that's a different story, and has nothing to do with the actual sale.