Ellis doesn't show up until the very end of the movie, but his conversation with Sheriff Ed Tom Bell helps tie together the movie—or at least as much as the Coen brothers will allow. It's basically Ellis' job as an old-timer (even older than Ed Tom) to tell Ed Tom to stop whining so much and to accept the world for what it is.
While Ed Tom thinks that evil of the world is getting worse and worse all the time, but Ellis quickly reminds him, "What you got ain't nothing new. This country is hard on people. You can't stop what's coming. It ain't all waiting on you. That's vanity."
In other words, Ellis reminds Ed Tom that the world doesn't depend on what Ed Tom thinks of it. No matter what happens or how many psychotic killers it holds, it's going to keep on turning.