Hi,
Yes you can die from pain. There is a know phenomenon called "Broken Heart Syndrome" where stressful situations such as the death of a loved one cause you to develop a heart condition that ultimately kills you. Most cases reverse with time, but some lead to further complications including low blood pressure, backup of fluid in the lungs, and heart failure. For more info, check out "Takotsubo cardiomyopathy"
Best,
Starlyte