UPDATED 9/2
As things stand right now...
At present, 39 Cubs minor leaguers (25 6YFA and 14 second-contract FA) are eligible to be MLB Rule 55 minor league free-agents at 5 PM Eastern on the 5th day following the final game of the 2018 World Series, and at least 52 (possibly as many as 57 - see list below) Cubs minor leaguers are eligible for selection in the December 2018 Rule 5 Draft.
So the Cubs have until five days after the final game of the World Series to either sign a post-2018 minor league free-agent to a 2019 minor league successor contract or add the player to their MLB 40-man roster, otherwise the player will automatically be declared a free-agent.