The Underground periodically checks in with the loot from their current heist. You may choose to cut and run and take the current loot, or continue the heist to get even better rewards. After completing a heist, a new one begins. It takes 9 total progress for a heist to complete.
The Underground makes 1 progress after each Player Combat Round. After a loss, they make 3 progress.
The Underground makes 2 progress after each Player Combat Round. After a loss, they make 5 progress.