Hi to all the members, I have just joined as I have a 1949 Super 50 that I am about to start a restoration on. It will be fun trying to find parts as I am in Scotland, not known for its hordes of Classic Buicks.
While it is true that Buick built about 656,000 units for the 1951 model year, there are not so many left.. What is left in the USA tends to be junk or already restored and expensive. But there a a few left that can be stripped for parts. Another thing to remember is that many parts on a 1950 Buick are interchangeable with Buicks from the late 1930s to 1953, and in things such as brakes, bearings, and other mechanical items later than 1953; and also interchange with other General Motors lines, particularly including Oldsmobiles for the smaller Buicks, and Cadillacs for the Roadmasters. The parts typically hardest to find are nice trim and body panels, as many are one year only, and all are prone to rust. The folks on this site will often know of reliable sources in Canada and the USA. And, of course, expect to dig deeply into your purse for the cost of shipping weighty items.
Good luck, and let us know what you are looking for.