Gardiner F. Pierce, a son of Gardiner Pierce, was born 14 Sep 1833 in Fall River, Massachusetts. He married Fanny Anderson. Gardner ended up in Buffalo, New York where he enlisted in the 26th New York Regiment at the start of the Civil War. He deserted at the battle of Second Manassas in September of 1862 and then disappeared from public records. His wife Fanny had him declared dead when legally possible, applied for his pension, and remarried.
A Second Update to William's Story
But, he was not dead! For reasons unknown, Gardner F. Pierce reinvented himself as THEODORE HALLSTED. He later is found again in the public records beginning in 1865. Various records have a birth date of around 1833 from Fall River, Massachusetts. In 1890 he appeared at a veterans rally as a former member of the 26th New York Regiment (no Hallsted appears in the official records of that regiment).
So the descendants of Theodore Hallsted carry Pierce Y DNA as a result of a name change; the use of an alias (Theodore Hallsted) by Gardiner F. Pierce who was born in Fall River, Massachusetts.