In the First Season episode "Symbiosis" The Enterprise is in contact with two alien races; the Ornarans and the Brekkians. As is explained in the episode, the Brekkians have exactly one industry: The production of Felicium, a drug the Ornarans are addicted to. The Ornarans produce everything else, which they trade to the Brekkians for the Felicium.
Pause here and consider: The Ornarans produce absolutely everything the Ornarans need. That means food, medicine, clothing, energy, tools, vehicles, etc. Absolutely everything. This becomes important later.
The Ornarans believe they have a plague on their world, and that the Felicium is a necessary drug to allow them to live. They don't realize it's simply a narcotic and the Brekkians are nothing but drug dealers.
Picard won't tell them the truth, because it would violate the Prime Directive. It's a moral conundrum, but that's the choice he makes. No problem. All is well, right?
The Ornarans no longer have the ability to maintain their space ships. (Reason not given.) So as their vessels break down, their ability to trade with the Brekkians will eventually fail completely. Picard had initially agreed to help them repair their ships, but changes his mind. Officially it's because of the Prime Directive, but the real reason is that the Ornarans will eventually be unable to obtain more Felicium and will thus lose their addiction, freeing them. Good for them... but...
Well, what happens to the Brekkians? Remember, they have no industry whatsoever, other than the production of Felicium. They don't grow their own food, make their own clothing, produce their own energy. They are utterly dependent upon the Ornarans. What happens when the Ornarans, critically low on Felicium, start breaking their addiction and realize they don't need Felicium after all? Even if, for humanitarian reasons, they agree to keep sending food and supplies to the Brekkians, that will only continue as long as their ships are able to make the trip. As they deteriorate... The supplies would stop. (No, the Brekkians do not have their own space fleet.)
This would force the Brekkians to start converting their industry over to their own needs, but this is not a quick process, and would require skills and knowledge that the Brekkians almost certainly do not posses on their own. Because Picard is leaving the system with no intention of returning, the Federation will therefore be standing by and doing nothing while billions of Brekkians starve to death as the planet struggles to shift to self sufficiency.
Certainly some will survive, and the exact number of survivors will depend largely upon how much food they have already stored and how quickly they can convert to agriculture. They may well gave considerable storage, we don't know... But we do know they aren't likely to know much about farming, nor will they have much capacity to do so anyway, being unable to farm using any kind of modern farming equipment because they just don't have it.
If I were to write a follow-up story, it would involve the Brekkians sending out some kind of planetary distress signal,which the Federation would respond to. (Picard should have provided the technical resources to help the Ornarans repair their fleet, but Season 1 Jean-Luc Picard is kind of a self-righteous jerk a lot... I liked him better in later seasons.) This is not a Prime Directive issue. The Prime Directive is about non-interference, but does not apply when assistance is requested directly. Also, these people are well aware of the Federation so it's not like there would be cultural contamination.
So Picard makes a decision that will result in the death of billions, but it's okay because they were drug dealers, apparently.
