I've put together a chart showing where defenses associated with Jauron have ranked since 2004, when Jauron was the Detroit Lions' defensive coordinator. He later became head coach in Buffalo from 2006 through 2009 before spending the past two seasons as defensive coordinator for the Cleveland Browns.
Jauron was a senior defensive assistant for Philadelphia in 2010. He was the Chicago Bears' head coach from 1999 through 2003. I didn't have room for rankings from those teams and could not easily access them for seasons predating 2001.
The Cleveland Browns fired Jauron after the 2012 season. The team was under new ownership and seeking new direction. The Browns' defensive ranking weren't bad.
The Rams are not looking for a new defensive scheme or for a defensive overhaul. They are looking for a coordinator to fit into their existing framework.