I always love it when I learn something new that I couldn't possibly have thought of except that I happened to be looking at the back of a football card.
I was flipping through my '88 Topps football set, and I noticed that Everson Walls (268), Bill Bates (269), and Michael Downs (270) were all undrafted. It made me wonder if the Cowboys ever fielded an all-undrafted secondary. Sure enough, per PFR, in the 1987 season finale vs. the Cardinals (which was not a strike game), the starting DBs were Walls, Downs, Vince Albritton and Manny Hendrix...all of whom were undrafted.
Coincidently, I watched Tom Landry's A Football Life on NFLN the other day, which talks a lot about Landry's system. Apparently, "The System" included not wasting many draft picks on defensive backs. In 1987, only two drafted defensive backs APPEARED in a game for the Cowboys all season...strike and non-strike games included.