"Once your registration expires, your vehicle becomes unregistered."
When I read the sentence, the word "unregistered" got me thinking, because "unregistered" means "not registered", in other words "never written on a paper or on any medium" In the case of cars, I would understand that an unregistered car would be a car which has just came out of manufacturing process, and has not been bought by anyone yet. And it will be registered when somebody buys it.
Or it may be that your move to another state, and in that case your car is unregistered in that new state, because it was never registered there. So it makes sense.
However, when it comes to a car which has already been registered in a book or other medium, the word "unregistered" sounds weird. We know that they were actually registered some time in the past, and -as part of that registration- they were appointed or given a time period. It is only that this time period has expired, but the registration is still there.
So, the registration has not disappeared or has not become extinct. In fact registration is still on the same paper (or whatever medium it was written on) with only a warning that time period appointed has expired.
To sum up, it is not the registrations that expire, but it is the time period that expires, and this time period is not the whole registration. It is only one of the many fields that comprise the registration which consists of many fields (name, date of production, brand etc). Even if that period has expired, the registration about that car is still there and the book or the database will continue to have a registration about that specific car. Just like a student who graduates from a school does not become "unregistered". His registration at the school will always stay there. An unregistered student would be one who has never started at that specific school.
Considering all these logic, why call these cars "unregistered cars" instead of something like "cars whose appointed time has expired"?