The problem comes in when they go to get the title transferred to them and get plates.. they will have to pay the back taxes.. if it is a few months over (say three), then they will have to pay for a year of taxes and it will expire after 9 months.
If its 4 years over, the buyer is liable for all 4 years plus the next year of registration. If you sell the car to a dealer, the dealer is required by law (in most states) to get the taxes up to date before they can sell it again. There are exceptions, such as if the car was junked at one time, it can be reclaimed, rebuilt, and licensed for just the current taxes.
In most cases, if the buyer takes the title to get license plates, and there is back taxes owed, they can legally go after the seller for taxes prior to the sale, but if the bill of sale specifies that taxes are not up to date, they cant (always, lawyers can do about anything anymore) go after you for the taxes.
It doesnt matter if the vehicle was driven as the vehicle tax is a property tax, not a tax for driving.. even though the money goes to the county's road repair.. makes sense eh?