In the very near future aliens show up near the Earth. After winning the trust of most right-thinking people they exchange some knowledge and goods.
Among the trades the aliens offer a reasonable amount of some other commodity in exchange for the mineral rights to a 1 km x 1 km stretch of land out in a desert somewhere. The land has a few trace amounts of minerals with some value, but nothing humans have the technology to extract in a profitable way at the moment. Agreements are signed and the aliens get the mineral rights.
The aliens create a cylindrical force field about a kilometer in diameter and start extracting the entire volume of earth as one huge core which is slowly and constantly streamed up through the atmosphere to where a giant mothership waits in geosynchronous orbit to collect it. The mothership never seems to increase in size or actually store this tremendous volume of rock anywhere so it’s speculated that there must be a wormhole on board which is transporting the rock elsewhere for processing.
As time goes by it becomes obvious that the aliens aren’t going to be satisfied with the first couple miles or so of rock. Eventually molten hot magma begins flowing up through the forcefield for days on end. It’s soon clear that the aliens are extracting everything all the way down to the very center of the Earth. It’s realized that this will geologically destabilize the region as a sort of super-volcano will probably form in the area once the core is removed and the forcefield is collapsed.
World governments are notified and negotiations with the aliens are started. Unfortunately negotiations with the aliens fail. The contract they signed was very specific and they aren’t going to let the humans out of it.
But things could be worse. The region being destabilized is pretty far from most civilization and shouldn’t have too huge an impact on human culture.
However things are worse. Several weeks later scientists calculate that the volume of rock and magma extracted has exceeded the volume of a cylinder stretching to the Earth’s center. Apparently the aliens are relying on the pressure at those tremendous depths to push the surrounding magma into the cylinder. In essence it’s like they’ve poked a drinking straw into the center of a water-balloon (without popping the balloon) and are relying on the pressure inside the balloon to push the liquid up through the straw. In a few years the Earth will be racked with massive ‘quakes as it’s entire geology destabilizes from the center outward.
Attempts to use military power fail as human nuclear missiles and other stratagems have no effect on the force field or the ship waiting in space.
To make matters worse, by sucking right from the center the aliens are depleting the nickle-iron core material first. With this material being siphoned off the Earth’s magnetic field is failing, allowing some of the harder forms of cosmic radiation to stream in. Things get increasingly worse as cancer rates rise and earthquakes rock the globe more and more frequently. Gradually, over the space of many years, tides get higher due to the Earth:moon gravitational pull being lower than it was in times past. In time the atmosphere begins to thin out as well, since there’s not so much mass to hold it in place any more
Humanity meets a slow and miserable end as their world crumples over the decades like a raisin.
In his final hours the last human survivor ruminates on why the aliens would do this to Earth when there are plenty of other planets in the solar system, not to mention asteroids, which could be mined without killing off the local populace. He (the last human is almost always male for some reason) conjectures about their desire to eliminate the competition early and a few other ideas, but rejects all them due to various technical arguments. In the end he’s stuck with the idea that the aliens are just kind of jerks and just don’t like humans all that much.