Localised death(necrosis) of heart tissue is referred to as

Sudden damage or localised death of heart tissue is myocardial infarction.

Myocardial infarction (MI), colloquially known as "heart attack," is caused by decreased or complete cessation of blood flow to a portion of the myocardium. Myocardial infarction may be "silent," and go undetected, or it could be a catastrophic event leading to hemodynamic deterioration and sudden death.