I wouldn’t say they are unstable. This is merely the flow of ions in response to a stimulus.

Each and every neuron is covered by a membrane. This membrane maintains an electrical gradient – a slight difference in electrical charge between the inside and outside of the cell. However this membrane is flexible and has gates/channels that allow the flow of certain chemicals inside/outside, so that the electrical gradient is maintained.

In the absence of any outside disturbance, the inside of the neuron is slightly polarized (difference in electrical charge). More specifically, the inside of the neuron has a negative electrical potential, compared to the outside. This undisturbed state is called resting potential. This resting potential is much needed, because it allows the neuron to respond rapidly to a stimulus. Any sort of excitation causes the neuron to open its channels.

GABAa receptors, in particular, contain Chloride channels, that allow the passage of Chloride ions in and out of the cell. When excited, the cell opens these Cl channels and allows the inflow of Chloride ions, increasing the negative charge inside the cell – hyperpolarization.

When a neuron initiates reaction to a stimulus it is through a propagation of an action potential. An action potential occurs when the neuron is depolarized (the slight negative charge inside the neuron is depolarized towards zero, until a threshold of excitation is reached, at which point the neuron fires rapidly to a positive charge). Again, we need depolarization in order to have action potential. If the cell is hyperpolarized (which is cause by antianxiety drugs like Valium, for example) the cell will not react. That is why overdose can lead to coma, or death.

I hope that was helpful, instead of confusing.