Second Base - Joe Quinn: -0.5. WAR
The first negative total WAR player to make the list is Joe Quinn who played second base for the Cardinals from 1893-1900. Over the course of his 2339 plate appearances with the Cardinals, Quinn posted just a .645 OPS. Against all odds, Quinn put together a 17 year career in the big leagues which is a reminder that baseball was a very different game back then.
Coming in second place in this hall of dishonor is Mike Tyson (no, not that Mike Tyson) at 1.2 rWAR for his time with St. Louis from 1972-1979. Pug Miles who just snuck into eligibility with 1,035 plate appearances in 1906 and 1907, took home bronze with 1.6 rWAR. Aaron Miles was a modern entrant into the fray at fourth place with 1.9 rWAR from 2006-2010.
Shortstop - Arnold Hauser: 1.0 WAR
The starting shortstop on this "squad" was a closely fought pillow fight to the death, but Arnold Hauser gets the nod at 1.0 rWAR from 1910 to 1913. Hauser hit just six home runs in his 410 games with St. Louis and his .609 OPS for the Cardinals certainly leaves a lot to be desired. However, Hauser's story was a sad one as he had his career derailed by the deaths of most of his immediate family including his wife and two children during his playing career.
Bones Ely, which is a pretty sweet name at the very least, put up 1.2 rWAR from 1893-1895 with Leo Durocher coming in third with 1.3 rWAR despite the fact that he somehow got named to an All-Star team with the Cardinals in 1936. Royce Clayton and David Eckstein were the closest "modern" players to inclusion at 9th and 11th respectively.