"Broken heart syndrome" is real, but it doesn't involve these tendons (which are known as the "chordae tendineae").
Broken heart syndrome, also called stress-induced cardiomyopathy or takotsubo cardiomyopathy, can strike even if you’re healthy. (Tako tsubo, by the way, are octopus traps that resemble the pot-like shape of the stricken heart.)
In broken heart syndrome, a part of your heart temporarily enlarges and doesn’t pump well, while the rest of your heart functions normally or with even more forceful contractions. Researchers are just starting to learn the causes, and how to diagnose and treat it.
Takotsubo cardiomyopathy is a weakening of the left ventricle, the heart's main pumping chamber, usually as the result of severe emotional or physical stress, such as a sudden illness, the loss of a loved one, a serious accident, or a natural disaster such as an earthquake. (For additional examples, see "Stressors associated with takotsubo cardiomyopathy.") That's why the condition is also called stress-induced cardiomyopathy, or broken-heart syndrome. The main symptoms are chest pain and shortness of breath.