USS Fleming (Olympic class)

The USS Fleming was an Olympic class Federation medical starship serving in the late 24th century. It was part of the medical fleet sent to Romulan space to help the survivors of the destruction of Romulus in 2387. It was destroyed by Nero's upgraded mining ship, the Narada. 

Wreckage of the ship was later found by other Starfleet ships in the Icari System in 2409. This was how Starfleet finally learned of the Fleming's fate.