What would happen if all bioelectricity in the human body shut down? (this is not the same as using electricity to kill someone - what happens when you electrocute someone is different)
I've answered as if this happens instantly. If it happens more slowly then go with hyponatraemia/hypocalcaemia as suggested above, because these are the main ions involved in the process described below.
First consider how electricity in the human body works normally. It's not like electricity in a wire. Your nerve cells work by the active transport of ions from inside to outside the nerve cell (in the axons - the long thin bit of the nerve cell). Active transport is where the cell membrane pumps particles against a concentration gradient. Without the active transport, there would be an equal concentration of ions on both sides of the membrane, because of diffusion. Your nerve cells use energy to pump ions out, against the concentration gradient, so that there are more on the outside than the inside. Ions have an electrical charge so this means there is a potential difference between the inside and outside of the nerve cell (i.e. electricity).
When a nerve impulse happens, the ions come flooding back in again. This starts at one end of the long thin bit of the nerve cell, and it triggers changes in the next bit of the membrane, which allows the ions in the next bit to flood in - this continues up the nerve cell. It's like domino rally - the dominoes fall in turn but the dominoes don't move along. Or like a Mexican wave in a sports stadium - each person moves up and down but stays in the same seat and the wave moves around the stadium. The ions themselves aren't moving up the nerve cell (not like electrons in a wire) they are moving from outside to inside, but the nerve impulse travels along the nerve like a mexican wave/domino rally. After the impulse happens, the cell membrane immediately starts pumping the ions back outside the cell, to be ready for another impulse.
So it takes a lot of energy to keep your nervous system in a state where it's ready for nerve impulses to happen. If this active transport of ions from inside to the outside of your nerve cells were to stop, your entire nervous system would immediately shut down and you'd die.
This doesn't just take place in nerve cells though. A similar thing happens in muscle cells. The reason why you get rigor mortis when you die is that the cessation of active transport of ions across the appropriate membranes puts the muscle fibres into a permanently contracted state. So not only would your nervous system immediately cease to function, all your muscles would cramp up, same as rigor mortis. Only difference is you're not technically dead just yet. The heart would cease to beat so all circulation would stop. Consciousness would cease instantly due to the nerves in your brain no longer being able to fire. Death due to lack of circulation usually happens after about 13 mins. At the point where the bioelectricity in the body shuts down, you would get all your nerves firing just once at the same time, as all the ions flow into the nerve cells and at the same time all your muscles cramp up. This would probably be experienced as a flash of literally everything including extreme pain just before your consciousness shuts down completely. In theory the muscle cramps would be extremely painful but the nerves won't carry that signal to the brain. The extreme pain would come from all the nerves that carry pain signals firing at once.
From the outside, the person would look like they completely froze up and dropped dead. Like rigor mortis. Instant death basically. It would look just the same as the avada kedavra killing curse in Harry Potter. In fact if you want a biological explanation for the avada kedavra curse this is most likely it. But for a high tech rather than magical way of killing someone, you'd give the bioelectricity explanation rather than it being magic. NOTE: it's still magical though, because there's no description of what mechanism is used to stop the cell membranes from actively transporting the ions across the membranes. But IMO that would only be an issue in a hard science fiction story. Future or alien tech can handwave this issue. Hostile alien/evil high tech bad guy has ray gun that causes nerves to stop actively transporting ions, which causes your entire nervous system to shut down instantly and for rigor mortis to happen before you're even dead. Sounds good to me!
ETA: the above is an A-level biology level explanation, aka year 13/university entry level. I have simplified the explanation compared to the detail that would be expected by an A-level examiner. The reality is more complicated than this but the general principle remains the same.
