I once saw a vole die of fear when it saw my dad (true story). I have heard stories of people dying of fright, but usually they were old or maybe had some kind of heart condition. I think over a long period being afraid can be harmful due to the long term effects of stress on the body. Ultimately it would lead to depression which could cause other illnesses. Not sure if it would be life threatening but could become chronic.
Seriously, I think it is possible – some people die of heart attacks after a shock. I *think* (but a not sure) that the adrenalin surge from the shock may set their heart racing and, if it is already disesed, this may unfortunately be enough to stop it working.
I am not a medical doctor, but I imagine that the stress associated with something really terrifying could cause a heart attack or perhaps a catastrophic drop in blood pressure (shock) which could lead to death. This would be much more likely in people with pre-existing health problems, especially heart conditions or pre-existing circulatory problems.
I think for most healthy people experiencing even very, very scary conditions (such as passengers on a plane involved in a rapid descent and crash landing) the body will prepare them to survive and escape. In evolutionary terms it would be very disadvantageous (to put it mildly) if an organism dropped dead as a response to danger. In other words, I think evolution has prepared us very well for scary situations, and a more usual response will be to efficiently escape or avoid danger.