The Pillage Planet mission is used by the Fury to extract funds from a controlled planet and reduce the population, weakening it in the process. When this mission is used, the following will occur:
The supplies and money will be received by all the player's starships that are in orbit. Starships will be filled with supplies and money in starship ID order. Once the hold space is filled, supplies will be converted to money. If there isn't adequate space in the starships for the money, it will left on the planet.
The starship performing this mission needs to have beams for this mission to be available. This mission is performed after starship movement. Any planet with colonists can be pillaged, including your own. No Diplomacy setting will stop this mission from being performed.
The Pillage Planet mission can not be performed by more than one starship at a time on a planet.
It should be noted that this is one of the few ways to reduce (and gradually eliminate) the number of Amorphous natives on a planet.
See also: Out of Fuel.