User Alienux had a good post about this, but I just want to further clarify what is surprisingly becoming confused by some fans. There is absolutely no evidence to suggest that candidates cannot kill other candidates or themselves. The only established rules on who can and cannot kill whom:
1. MIB couldn't directly kill Jacob (he needed a loophole to do so, and found one)
2. Richard can't kill himself (but can be killed by someone else).
3. MIB can't kill the candidates.
4. Someone (candidate or non-candidate) cannot be killed if the island isn't done with them.
It has been established multiple times that someone can't die if the island isn't done with them, regardless of if they are a candidate or not. Ilana (not a candidate) only died once "the island was done with her" as they made clear. Jack was unable to kill himself because the island wasn't done with him yet. There was no indication whatsoever that he couldn't kill himself just because candidates can't kill themselves.
Therefore, we essentially know this as well:
1. Candidates can be killed by other candidates (Ben killed Locke)
2. Candidates can be killed by non-candidates (Mikhael killed Charlie)
3. Candidates can kill themselves (Michael killed himself - once the island wad done with him)
Keep in mind, Sayid (a candidate) died either at the hands of Sawyer (another candidate) because Sawyer detonated the bomb, or at the hands of himself (also a candidate) because he grabbed the bomb knowing he would die.