The SS Californian is infamous for having been near the Titanic when it sank, but not coming to its aid until it was too late. Three years after the Titanic, the Californian sank too.
Multiple bad judgment calls led to the Californian not helping the Titanic: the ship's radio was allegedly shut off for the night when the Titanic hit the iceberg, and when the captain was awakened by the flares the Titanic had been setting off, he assumed that they were just fireworks. By the time the SOS messages finally came through, it was too late.
However, the Californian wasn't long for this world either — it sank on November 1915, torpedoed by a German submarine during WW1.