Though not running for president in 1872, he received 42 of the electoral votes that otherwise would have gone to Horace Greeley, the Democratic candidate who died shortly after losing the popular election. In that election, Hendricks received more electoral votes that election than any other Democrat -- Benjamin Brown of Missouri got 18 electoral votes, Charles Jenkins two, and David Davis, one -- though of course the Republican candidate, US Grant, won the electoral college with 286 votes.
In 1876, Hendricks was the Democratic vice presidential nominee, and had the office stolen from him every bit as much as Samuel J. Tilden lost the presidency through fraud, though that was merely incidental -- no one sets out to steal the vice presidency. In 1884, when Grover Cleveland became the first Democrat to win the White House since James Buchanan, his running mate Hendricks became the first Democratic vice president since John C. Breckinridge, unless you count Andrew Johnson.
Hendricks died in office in November 1885 after serving not quite nine months, becoming one of a long string of pre-1920s vice presidents to die in office, who also included George Clinton, Elbridge Gerry, William King, Henry Wilson, Garret Hobart and James Sherman. Hendricks' colleagues in government clearly thought enough of him to honor him in an unusual way -- in fact, in a unique way for vice presidents. In 1886, his face appeared on a 10-dollar silver certificate (pictured). Among vice presidents who were never also president, he is the only one thus honored.