If you watch the chair torture scene and pay close attention to the lines, Elektra cut her own ear lobe off as a means to manipulate Renard into thinking she had been victimized by his men.
Uuh ? Are you sure ? As far as I can remember, she indeed cut off her own ear lobe AFTER turning Renard, and she did it herself because he didn't want to harm her, and because she considered it necessary to put pressure on her father.
I don't have the DVD at hand right now, but I shall check as soon as possible.