It's more that every cell has to maintain a voltage difference between the inside and outside ("membrane potential"). A healthy cell does that constantly using "ion pumps" that use chemical energy (ATP) to increase the potential.

If that potential falls below a certain threshold, certain molecular mechanisms (voltage-sensitive ion channels) inside the cell are triggered that lead to ejection.

Interestingly, are also other mechanisms (pressure-sensitive ion channels) that will "intentionally" make it harder for a cell to maintain its potential if it's already weakened or if the surrounding region is very crowded.

As such, I think the effect of current would depend on the way how it would change the voltage differences of the individual cells.