I have the same problem - it's really disgusting when they leave their slime everywhere. Sometimes one doesn't get out in time before the girls get up - they will kill it, but don't seem to want to eat it.
I haven't really found a solution. I do use (sparingly) a product in the veggie patch called Multiguard - active ingredient is chelated iron which attracts slugs who crawl off and die. It states it is wildlife friendly but I am still wary of trying it around the run. The chickens can't get into my veggie patch. I guess they probably wouldn't eat a dead slug anymore than they will a live one. But I feel cautious about it.
I hope some other BYCers have some advice for us!