While pretty ubiquitous in Europe after WWII, the rear-engine car never caught on here in the States. Oh sure Tucker tried to take on the established auto industry with his rear-engined Torpedo, and Chevy took competing with Volkswagen to absurdly literal extremes with the Corvair, but otherwise the rear-mounted mill has not proved a popular placement with American manufacturers.
That might have been different had one company continued both its dalliance with a European car maker famous for its rear-engine engineering, and just plain staying in business.
From Studegarage:

In February, 1959 Curtis-Wright bought a new Lark with a Champ 6 engine from a local dealer and modified it.  A used engine from a 1953 Porsche was rebuilt by Porsche and installed along with the torsion-bar rear suspension and transaxle.  Wheels and gear reduction boxes from a VW bus were used to optimize the drive line.  This engine was placed in what had been the trunk of the Lark after removing the Champ 6 and automatic transmission from the front of the car.  In addition, since Curtis-Wright had taken out a license to build Wankel rotary engines, an adapter was prepared to install a small Wankel engine in place of the Porsche engine.  This car may have been the prototype for the sub-compact touted two years later.

The Curtis-Wright Corporation had purchased a controlling interest in Studebaker-Packard in the late ’50s, and sought to breathe life into the flailing company. It was under the CW management contract that Packard’s famous Detroit plant was sold to Chrysler, and import agreements with DKW and Mercedes Benz were inked. Perhaps most interestingly, at the same time Curtis-Wright was attempting Studebaker’s turn-around, they were also working on prototype hover cars for the U.S. Military.
Before the Porsche-engined Lark, Studebaker had engaged Porsche directly to develop a new sedan. The resulting Type 542 featured a rear engine and a low-slung body. The car was reviewed by Studebaker’s then director of experimental engineering, John Delorean – yep, that guy – who found its handling and general demeanor to be lacking. The project was dropped and Porsche would stay away from 4-doors until 2003 when the Cayenne sport utility was introduced.
Image: Dedeporsche