From this question, it seems quite clear to assume for the purposes of this question that Borg are considered 'living'.
At the beginning of the episode (Descent Part 1, TNG) we see the TNG crew encounter some Borg at an outpost. Data then proceeds to strangle the Borg, the reason being later on because of the negative emotions being channeled to Data by Lore from the emotion chip. I think it is safe to assume that that Borg was killed.
My question is: how was Data able to kill that Borg? He explains quite clearly on multiple occasions (notably in The Most Toys) that the fundamental basis of his programming is that he has a respect for life and therefore cannot kill (although by the end of The Most Toys there is a question raised over whether or not he was going to kill a person). Hence, Data seems to have gone against his fundamental programming. How can this be so? I have envisaged two possible solutions, but I don't claim that these are the only possible solutions:
The Borg are not considered to be 'life forms' by Data, and so he can kill them.
The emotion chip can override Data's fundamental programming. This isn't quite such a silly idea, as what if he got annoyed by a fly and swatted it? (Note that later on when he is on the Holodeck and not receiving input from the emotion chip, he is actually not interacting with a real Borg, meaning he could therefore kill that Borg repeatedly - it's just a computer program. ) The only issue I have with this is that it seems odd for Dr Soong to create a chip that would override Data's fundamental programming, although it would make him more human, or if Lore had tampered with it to have this affect.