The Talaxian asteroid colony was a settlement of about five hundred Talaxian exiles hidden inside an asteroid in the Delta Quadrant, which Neelix helped to defend in 2378 and then made his home.
The colony appears in Homestead, one of the final episodes of Voyager. Its people fled Talax after the Haakonian conquest and travelled tens of thousands of light-years, driven from one world after another, before hollowing out an asteroid under their leader Oxilon.
Neelix meets the widow Dexa and her son Brax there. A mining consortium headed by Nocona owns the field and intends to break up the asteroid. Since Starfleet rules limit what Janeway may do, Neelix organises the colonists to install shield emitters themselves, with Tuvok's quiet advice.
The defence holds. Janeway asks Neelix to act as the Federation's ambassador in the region, giving him a reason to stay with Dexa. The crew line the corridor to see him off.