In Act 4, you can come across the ghost of Captain Rumford in the Silver Spire. In all my playthroughs, I can't seem to find the part where he dies. How/when did he die?
If you start the mission "Trailing the Coven" and leave New Tristram heading towards Old Tristram, you can find Rumford's corpse on a bridge not far from the town gates.
Clicking on him will make your character deliver a short eulogy (in my Witch Doctor's case, he said "Rest easy, friend..."). There's no in-game dialog that explains exactly how he died, but given the events of the mission prior, it's likely he was slain:
while trying to protect the town from the cultists who kill Deckard Cain and take Tyrael's sword fragments.