According to family lore, Peter Conover Van Doren (my third great grandfather on my mother's side) loved to gather his grandhildren and great-grandchildren around him, and tell them about grandparents several times removed.
Great Grandfather Van Doren told the tale of of his wife's great-grandparents on the mother's side bearing the name of Rogers. The Rogers emigrated from Ireland - a mother, father, and a daughter. Soon after they departed, a violent storm crippled the ship. Mr. Rogers died and the ship's stores of food and supplies were destroyed. In order to survive, three passengers were in turn killed and eaten. The survivors drew lots and Mrs. Rogers was chosen to be the next sacrifice. She asked for one hour to pray, which was granted. When but a few minutes of the time remained, the sound of a cannon came booming over the waters, conveying the glad tidings that they were discovered, and her life was spared.
On arriving in the American colonies Mrs. Rogers (probably named Mary Elizabeth Rogers) settled in Pennsylvania with her only daughter Elizabeth met and married Patrick Meloy, a Frenchman. Around 1800, Patrick, Elizabeth, and family moved to Warren County Ohio where their daughter, Amy Meloy, met and married Ebenezer Hathaway. Ebenezer and Amy's daughter, Margaret Hathaway, met and married, Peter Conover Van Doren, our storyteller.
I searched for some sort of independent validation of this story but found none. I did not locate any records for Elizabeth Rogers that predated her marriage to Patrick Meloy. No passenger manifests, no validation of Mr. Roger's death at sea, no validation of the cannibal lottery. Like most family tales, there is probably some grain of truth but not the whole truth.
The Rogers would have sailed after 1762 when Elizabeth was born, and before 1784 when which Elizabeth married Patrick in Pennsylvania. From the dates, we can say that the Rogers had survived the Great Famine (1845-1852) where 1/3 of Ireland's population starved to death and another 1/3 fled.
Most of the Irish were Catholic and the English government forbade Catholics from owning land. So there wasn't much future or opportunity in Ireland. Many English landowners would pay passage to the colonies to get the Irish tenant farmers off their land. William Penn welcomed the refugees to the Pennsylvania colony where freedom of religion was allowed.
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"The Van Doorn Family in Holland and America, 1088- 1908" by A. Van Doren Honeyman, Honeyman's Publishing House, Plainfield, NJ 1929 Page 489-490