In the course of helping to investigate a network of caverns in a planetoid for dilithium deposits, Neelix is attacked by a previously undetected alien and left in a state of shock. He is beamed directly to Sickbay where it is found that his lungs have been teleported out of his body. The Doctor keeps him alive by projecting a pair of holographic lungs into his torso using Sickbay's holographic emitters.
Another away mission is quickly organised to find the perpetrator and retrieve Neelix's lungs. They return to the planetoid and discover an alien facility behind sophisticated cloaking technology, and conclude that the facility is being used to store organic material, particularly respiratory organs. In a hostile encounter with an alien, they obtain the alien device used to remove Neelix's lungs and find it to be a highly advanced medical and surgical instrument.
The aliens escape the planetoid on a ship, and Voyager goes in pursuit. Eventually Voyager catches up with them and Captain Janeway orders the abduction of the two alien life forms aboard the ship.
An interrogation reveals that the aliens belong to a race known as the Vidiians, who have been suffering for generations from a disease called the Phage. The aliens explain that the only treatment for this disease is to replace degenerating organs, and they do so by harvesting organs from other beings (usually cadavers, but if an organ is needed immediately, they will steal organs from living creatures).
It transpires that Neelix's lungs have already been transplanted into one of the aliens, and Janeway's ethical obligations force her to let them go rather than condemn the alien to death by retrieving the lungs. In response to this leniency, the aliens offer to help Neelix, and are able to provide the medical expertise necessary to perform a transplant from another crew member, a procedure which was originally prohibited by anatomical incompatibility.
Neelix receives a donor lung from Kes.