Given the discussions going on over at the BGG forums on this, it seems like there needs to be a specific clarification from Lukas, official errata, or something similar on this set of interactions before everyone will be satisfied with an answer and agree on how to handle this.
First, the cards and relevant text from the cards in question, to make sure that everyone's on the same page. First the ICE:
Chum: Subroutine: The next piece of ice the Runner encounters during this run has +2 strength. Do 3 net damage unless the Runner breaks all subroutines on that piece of ice.
Data Raven: When the Runner encounters Data Raven, he or she must either take 1 tag or end the run.
Tollbooth: When the Runner encounters Tollbooth, he or she must pay 3 Credits, if able. If the Runner cannot pay 3 Credits, end the run.
Data Raven and Tollbooth each carry a single Subroutine, but the details of those Subroutines are trivial for this question; only the presence of the Subroutine in either case is necessary, due to the Icebreaker in this situation:
Femme Fatale: When you install Femme Fatale, choose an installed piece of ice. When you encounter that ice, you may spend 1 Credit per subroutine on that ice to bypass it.
Now we set up the situation. The server that is being run against has two ICE installed. At the first layer, Chum is waiting for the Runner. The following ICE could be either Data Raven or Tollbooth; either of those creates this same interaction. Finally, the Runner has Femme Fatale attached to the Data Raven/Tollbooth.
The Runner begins the run, and does nothing about Chum, just trudging right through it. The subroutine is not broken, so now Chum is watching for its trigger to occur. Corp player rezzes the Data Raven/Tollbooth. Now we get to the questions:
1) Data Raven and Tollbooth each have a single subroutine on them, so Femme Fatale's special effect allows them to be "bypassed" for 1 Credit. Does this mean that a) the subroutines are "bypassed", a term which we have no definition for or information about in the context of subroutines whatsoever, b) the subroutines are broken (the wrong word was used in this case), or c) the entire ICE is bypassed, a term we have no definition for in the rulebook?
2) If 1b is not the way that Femme Fatale behaves in this situation, does this play out as: a) Data Raven or Tollbooth execute their on-encounter triggers, ICE is bypassed for 1 Credit by Femme Fatale, Chum deals 3 net damage because the subroutines were not broken; b) Data Raven or Tollbooth are bypassed and on-encounter triggers do not execute due to Femme Fatale bypassing the ICE, Chum deals 3 net damage because the subroutines were not broken; or c) Data Raven or Tollbooth are bypassed by Femme Fatale with no effect, Chum looks for a third ICE in the line because the second one was bypassed.
If 1b is the way that Femme Fatale behaves, then presumably the effect is d) Data Raven or Tollbooth execute their on-encounter triggers, Femme Fatale breaks the subroutine for 1 Credit, Chum is satisfied and does not go off at all.
I guess the underlying question in all this, really, is what exactly "bypass" means, and how it interacts with on-encounter triggers.