Check out this 1993 Lincoln Mark VIII with doors that retract to the underside of the carriage.

Lincoln commissioned Joalto Design to modify the car after worrying about its ability to fit in tight parking spaces. Joalto’s solution was to have the door slide under the car, but Lincoln didn’t go for it and ordered the vehicle destroyed. It lived on to now appear on eBay for $20,000 (so far). eBay listing