It can be very stressful - dealing with customers who aren't very happy. I don't know if I've ever had death threats, but I have been threatened with violence by people who assume you are in the same city as them. I get sworn at a lot. But you have to remember the abuse is usually in the heat of the moment, it's nothing personal, and the person wouldn't know you if they fell over you in the street. You have to deal with things without feeling customers' comments are not a direct attack on you or your company - and, of course, lots of people are very loyal to their employer.
Some workers find they can deal with angry callers better than others.
If you find it difficult, if you refuse to apologise for something that isn't your fault or the fault of your company, then a call centre isn't the place for you. There are plenty of defusing techniques to change the course of a call. Apologies, for example. If you say 'sorry', that doesn't sound like you mean it. I'm sorry I dropped a concrete block on your foot' then the apology is instantly more personal and appropriate.