Here is what will happen and (in some cases) might happen after the conclusion of the World Series...
At 9 AM (Eastern) on the day after the final game of the World Series, the eight Cubs MLB Article XX-B free-agents (Jake Arrieta, Alex Avila, Wade Davis, Brian Duensing, Jon Jay, John Lackey, Rene Rivera, and Koji Uehara) will be declared free-agents (players do - NOT - have to file, it's done automatically) and will be removed from the Cubs MLB Reserve List (40-man roster) at that time.
Clubs retain exclusive negotiating rights with their own Article XX-B free-agents until 5 PM (Eastern) on the 5th day after the final game of the World Series (the first five days of free-agency are known as the "Quiet Period"), after-which the player can sign with any MLB club.