From the UFAQ:
If the Runner uses Fall Guy to prevent Bug Out Bag from trashing itself, do they still draw cards?
Yes. Trashing Bug Out Bag is part of the effect of the ability not a cost or condition.
So, let me get this straight... Nothing on the card says anything about removing counters. So if you prevent the trash, you can just keep it and use it again. You could load it with, like, 7+ counters, and use it alongside 3 Fall Guys as a janky semi-permanent draw engine. Load it once and you can end 4 turns with no cards in hand to draw 7+ cards and be good for the next turn or two. That's a lot of draw. Enough, actually, to draw most of your deck and be considered your main draw engine.
As long as your deck has a consistent way of getting rid of spare cards before the end of the turn, like for example Faust, Bookmark, Severnius Stim Implant, The Noble Path or maybe some self-damage tricks.
Another interesting synergy is Safety First.
At the end of the turn, it's checked if your grip is empty. If it is, both Safety and BOB trigger simultaneously. The runner simply chooses to resolve Safety first (pun intended), gaining 1 card and then still gaining X cards from BOB despite his hand not being empty anymore, because it was empty when the end-of-turn triggered. So the runner ends up with X+1 cards in grip.
That might actually do some good work in an Adam deck that burns cards fast.