The way I think of it is this...
You have a closer who two seasons ago was one of the best in the business despite his ridiculous walk rate. He might revert to that form or he might continue to suck. Chances are it's somewhere in between. Instead of eating all of the remaining contract (I think it's around $15MM or so) and allowing him to pitch next season, you look at this season (in which the Cubs were projected to win just 70ish games) and you let him keep plugging along. If he's fantastic you can trade him at the deadline or in the offseason. If he's crap you can release him at the end of the season if you can't trade him during the offseason, and since the team wasn't going to make the postseason, it doesn't matter whether they won 60 games or 80 because neither was going to get them in the show.
You do whatever it takes to try to salvage the guy's value before you cut him loose. The salary is a sunk cost, but you have to try.