People do die of loneliness but it's not usually the loneliness that kills the person.
Most people who become lonely end up committing suicide after awhile because of the mental torture that someone experiences when lonely.
Some people just can't stand being lonely while others are okay with being alone.
Most humans are social animals and need social interaction to survive and without that social interaction many people give up and want to end it all.
Other times the depression may get to the person so much that it messes with the persons heart and blood pressure because depression as well as anxiety can raise a persons blood pressure without them knowing about it and that high blood pressure can lead to heart disease, strokes and even a heart attack which could kill the person.