The Talaxian asteroid colony was located on an asteroid in the Delta Quadrant. It was colonized by about 500 Talaxians who left their homeworld after the Haakonian Order had conquered it around the mid-24th century.
The USS Voyager visited the colony in 2378 when they detected several Talaxian life signs nearby. When Voyager arrived, however, no response to their hails were received. The crew decided to send an away team in the Delta Flyer to investigate. Unfortunately, a group of aliens were conducting a mining operation in the asteroid field and the Flyer was hit by a Thermolytic charge, causing it to crash on the Talaxians' asteroid. The crew was only slightly injured, but the Talaxians were suspicious of them and confined them. After determining that the Flyer's crew was not a threat, they were released and asked to leave.
Unfortunately, the aliens conducting the mining operations had plans for the Talaxians' asteroid. They needed the asteroid because it contained a majority of the belt's minerals needed to power their ships. When one of the aliens nearly assaulted Dexa, one of the Talaxian residents, Neelix stepped in to defend her and her son, Brax. Captain Janeway attempted to negotiate with the miners to save the asteroid, but to no avail. Instead of evacuating, however, Neelix convinced the Talaxians to set up a shield grid in order to prevent the miners from destroying the asteroid. With help from the Delta Flyer, the plan succeeded and the miners abandoned their operation. (VOY: "Homestead")