There never was any need for death at Tarsus IV anyway. A food shortage isn't dealt with by halving the population, it's dealt with by halving the rations. And if that doesn't help, then halving the population
can't help in any fashion, either.
That is, if the population's survival truly depended on food "stores", this implies the planet was sterile (if it wasn't, 8,000 people could survive indefinitely by going outside and eating the local equivalent of berries and snails). If all food indeed were lost, then there are two scenarios: a scheduled resupply (or one specifically requested for the occasion, with a roughly known schedule as the result), and no resupply. For the first scenario, rations can be stretched - that's how human physiology works. For the second, everybody is dead already, and leaving 4,000 alive for a brief while (supposedly to eat the other 4,000) will change nothing.
How could there be "no resupply", since humans do need to eat? The one possibility is that there are crops to be harvested. And that already debunks the "sterile world" scenario, plus suggests a schedule where the "resupply" interval can be at most a year (Trek humans wouldn't have it otherwise - they always live at one AU from the star). But the length of the crop interval as such is irrelevant: in any case, it only involves halving of the resources, which can be dealt with by halving the rations, which in turn is always survivable for humans.
So, technobabble to the rescue. Sort of.
Timo Saloniemi