Well, mine didn't run long enough for anything to become a major factor. Still, there is the chance that the players realize that there's no way to get off this merry go round except by either jumping plot and taking your chances in the Zone, or, well, death.
Of course, though it's not in the book, you can escape if you find a Fringe portal. Getting back to where you started... not so much. If you can go through the portal, it will sever your connection to the plot. Hopefully the world you get off at is a nice one.