Charles Widmore never played by the rules…
So from what we know so far, candidates cannot be killed. Well, Charles told Ben to kill baby Alex. Instead Ben kept her, and said she was his daughter.
This is copy & pasted from Lostpedia:
20 ROUSSEAU Cave/Lighthouse Probably Alex Rousseau or Danielle Rousseau.
So hence, either Alex or Danielle was a candidate, and candidates cannot be killed it seems to be against the rules.