I guess medically you can, but isn't that really a cop out of life? I mean, if your heart is broken, that isn't really a reason give up on life altogether is it. When my dad died, my mother was really broken hearted. She'd been 11 when she fell in love, and they were together till he died when she was 59. But she lived for my sake, because she knew he wouldn't want her to pine and just not take interest in life again. So I think it's really a case of not being strong enough to work through the pain.
That said, sometimes it can happen, especially when the person is really old and can't face life alone.