Would that have been a Triumph Mayflower? If so, there’s one for sale on eBay. Unfortunately, the guy doesn’t have a single picture.
http://cgi.ebay.com/ebaymotors/Cars-Trucks___1951-Triumph-Mayflower_W0QQitemZ300275218336QQddnZCarsQ20Q26Q20TrucksQQddiZ2282QQcmdZViewItemQQptZUS_Cars_Trucks?hash=item300275218336&_trksid=p4506.c0.m245&_trkparms=65%3A-1|39%3A1|240%3A1318
Here’s a vintage print ad, and although they called it a “Sedan”, it looks like what one would call a station wagon.
http://www.adclassix.com/ads2/51_triumph_mayflower.htm
If there’s one left, it ain’t extinct (yet).
Also see aldiboronti’s and Fear Itself’s links.
Car collectors often have oddball vehicles in their collections. There’s a casino in Biloxi, MS that used to have the owner’s huge car collection on display (same guy owns one of the big ones in Las Vegas where I believe he has a big display also). There were lots of neat cars in his collection. The oddballs were a Yugo and a early 80s Ford Fairmont, which was nothing special, but it was the 10,000,000th car to roll off the Ford assembly line or something like that. As long as this guy keeps these cars, or sells them to other museum type collectors, they’ll never be extinct. Hell, if you search on Google, you’ll find that the Chevette has a huge following and you’d think those would’ve all fallen completely apart by the late 80s.
My closest nomination would be the Chrysler Turbine car. Only 55 were produced, and there was a big promotion where people could enter a drawing to get to drive this car for a couple thousand miles. They were distributed all over the country and people took turns driving them. At the end of the promotion, Chrysler decided that it wasn’t economically feasible to produce the car and ordered that they all be destroyed.
Nine of these cars survived and of the nine, six of them had the turbine engines removed. These cars all went to museums and one private collector. This leaves three that still start up and drive. The wikipedia article (Chrysler Turbine Car - Wikipedia) says that one of these is transported to shows around the country. So we have actual documentation of where each and every one of these surviving cars is located, and should a series of catastrophes happen, we’d know if this car became extinct.
I realize that this wasn’t a mass-produced car, but since it was such a big promotion back in the early 60s and everybody knew about it, I think it would qualify (if it ever actually became extinct).