Yes, although it's not a subject that has prompted much clinical research, much less rat studies of fatal heartbreak.
A chief medical examiner once wrote to me describing a poignant case of what appeared to be a fatally broken heart. This pathologist had recently performed autopsies on an octagenarian couple who died on the same day. The man, with a long history of heart disease, was found dead out in his farmyard. His wife, dead a shorter time, was found on the front porch, at an angle showing that she would have seen her husband's body. Next to her was the bell she had brought to summon him to the lunch sitting on the table inside. Her autopsy showed no obvious cause of death other than a heart that had stopped.
What happens in a case like this? We can only speculate, since it's not possible to study this phenomenon in animals, and it's hard to glean much from an autopsy. But there are documented cases of sudden cardiac arrest following powerful emotional distress. What probably happens is that ongoing stress, following a traumatic event or loss, adversely affects the cardiovascular system. Stress does its damage over time by slowly chipping away at the integrity of the blood vessels, causing subtle damage that sets them on the path to atherosclerosis, or "hardening of the arteries."
During a crisis -- including an emotional crisis -- the sympathetic nervous system is also involved. This system mediates the "fight-or-flight" response by secreting stress hormones such as adrenaline, also known as epinephrine, along with the related norepinephrine. These chemicals stimulate the heart and prepare the body -- either to do battle or run for one's life.
Under normal circumstances, the levels of those two chemicals are choreographed with wondrous precision. The last thing you'd want to do is to get the sequence of cardiac stimulation out of whack, because disruption of these cardiac stimulators can lead to serious consequences. But such loss of coordination is precisely what happens during immensely strong sympathetic stimulation to the heart, resulting in difficulty pumping blood, especially when the heart muscle is already diseased. This state, known as "fibrillation," can prove fatal.
So, yes, it's certainly possible to die of a broken heart, but it usually takes a very major break and an already weakened heart.
When people think of fatal heartbreak, though, other less plausible scenarios often come to mind. If someone is so devastated by a loss that he or she stops eating, for instance, jumps off a building, or, instead of sprinting away from a predator, turns around to tell the beast a tale of woe, that person is not going to fare well. But that's not the kind of fatal heartache we are considering here. Nor is it the case of a guy who gets catastrophic news and, wailing, clutches his chest and keels over dead from sudden cardiac arrest. While there have been such cases following powerful emotional distress, they are extremely rare, more common to the movies than real life.
Robert M. Sapolsky is professor of biological sciences and neurology at Stanford University and the author of Why Zebras Don't Get Ulcers: An Updated Guide to Stress, Stress-Related Diseases, and Coping