UPDATED 6-7-2019
As things stand right now...
38 Cubs minor leaguers (one Article XX-D FA, 27 6YFA, and ten second-contract players) 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 2019 World Series, and 71 Cubs minor leaguers are eligible for selection in the December 2019 Rule 5 Draft.
So the Cubs have until five days after the final game of the World Series to either sign a post-2019 Rule 55 minor league free-agent to a 2020 minor league successor contract or add the player to their MLB 40-man roster, otherwise the player will automatically be declared a free-agent.