The D6 system had a mechanic in place where a character could collect dark side points and turn to the dark side. A PC steps on enough babies (and enjoys it) and the GM takes their character away for good.
I never played it, but I gather that the D20 engine had something similar in place - be too evil, lose your character.
I haven't found anything in EotE that's similar. Did I just overlook a rule somewhere? Or did FFG not build that into the engine.