Peter Chiarelli missed the playoffs this year and was gone, two years after making the cup finals and four years after winning the cup. He was two wins away in 2013 from essentially duplicating what LA did. If LA misses the playoffs next year as well, you bet DL could be gone. It's certainly not a foregone conclusion he stays.
As for Kopitar, LA is not going to deal away their best centre and the best forward of their cup winning years if they are in the hunt for a playoff spot next year. They should be as well, barring a collapse even worse than this year. Trading Kopitar just won't happen unless LA completely implodes next season. If you think it will, it's a dream.
What we don't know if what Kopitar wants and how set on it he is. But given his age and what guys like Toews got recently, if he wants an eight-year deal bad enough, he knows he can get it. If LA doesn't want t, he can go to UFA and get seven years. Someone is going to open the checkbook for him.
If Kopitar does leave is it "the end of the world"? No, of course not, but LA will be without their best forward and have an aging core with only a few guys like Toffoli and Pearson showing strong top two upside long-term. And they won't have their 1st in 2016 either. Unless DL starts pulling off deals to bring in some top end talent, LA is going to have a pop gun offense in two years without Kopitar, largely a one-line team (the 70's line). And you will not find a Kopitar on the trade market or in UFA. Name the last player of Kopitar's market to hit UFA? The last time someone like him was traded was Thornton, and that was a decade ago.