Honestly, it's the moderator's decision. For instance, when it came to homophobic behavior, I always banned the player. Why? Because I have zero tolerance for homophobes. I'd categorized this as "bullying", I suppose you could say since it can affect the person. But then again, I wouldn't think anyone would think bleach, unless the person has a long history of bullying.
Talking about people saying to someone "go and kill yourself" or something along that line, there is a player on OPPrison who calls me a "nolifer" (If your heart is beating, you have a life, my point of view) and said "Go and jump off a brigde no one loves you tubeless" which I found funny since he was Z before me, he bought trillions of from Cryptic with irl money and I just happened to play it at the time when he came online at that time of the day. I can't provide screenshot right now due to me posting this from my phone, but I will once I find the screenshot on the computer I played on at the time. (My parents are divorced so it might be at my computer that is at my dads house, staying this week at my mothers house)
Well, I agree, this has got to be taken seriously. As said above, it does depend on the moderator and how severely they consider cyberbullying as an offence. No matter what others may think, cyberbullying really is a problem. I've banned quite a few people for cyberbullying during my time as a moderator here, all with a valid reason. Frankly I believe that these kinds of people are not needed on Mineverse.
I just got new enlightenment on this situation. Life threats or telling others "to go kill yourself" is very immature, uncalled for, mean, and like @Christi said cyber bullying. A player has recently been saying kys when ever he is talking to me or his message is said towards me. For those of you that don't know or couldn't figure it out, kys stands for "kill yourself". All in all support, death threats need to be bannable, or at less punishable.