What do the vehicle manufacturer's do with the vehicles they do not sell from a previous year?

The dealer sells last years models as leftovers. Usually the manufacterer will put extra incentives either to the dealer in "dealercash" or to the consumer in the form of rebates.

I sell Volkswagens (my day job, ugghh)... and we have always sold all of our cars, even if we have to give deep discounts to do it. SOme manufacturers I would imagine sell their cars cheap to rental companies or donate them to charitable organizations for tax purposes.

Unless the manufacturer takes the vehicles back from a dealer and sells them somewhere else or has them destroyed the vehicles get sold in the normal manner, no matter how long it takes. Fleet and rental buyers don't generally buy leftover vehicles. If the vehicle sustains serious damage, in some cases it will be fixed and sold as used or destroyed. Laws vary by area, of course.