The crew of the Nebuchadnezzar (and people in Zion) dies in the real world when they die in the Matrix.
Does this also happen to the "human batteries" in the pods? Say that Joe walks under a bus when crossing the street (in the Matrix) and dies. Does he also die in the pod?
This would be a horrible waste of energy for the machines - the body of the careless pedestrian is still full of energy to harvest.
The Matrix is a closed system over which the Architect has near-total control. Logically speaking, normal ("blue pill") people don't need to die inside The Matrix until it's time for them to die, at which point they'll conveniently meet with an accident or illness or whatever to free up their pod.
So, how might someone die prematurely? That's where the Zionese rebels come in. They're hooked in from outside the system of control. They can kill blue-pills before it's their time to die, and that's one of the main reasons that they represent an escalating threat to the stability of the Matrix. More rebels means more conflict which means more prematurely dead humans.
As to what happens to them when they die, there's no good reason to assume it's any different from what happens to the rebels when they die. The body cannot survive without the mind. The only difference is that they now get liquidised and fed to the remaining inhabitants and a new embryo takes their pod.
We see this process taking place when Morpheus and his crew trick the Matrix into thinking that Keanu has had a heart attack.
