The Anchorage was initially conceived as a fallout shelter for the League Government. A fallback or evacuation point that was quite difficult, if not impossible, to reach without the proper heading and navigational algorithms. For fully understandable reasons (ie the difficulty of getting to the site), the station was shutdown leaving a perfectly good station drifting in an unapproachable system.
After a century or so of neglect, the Director of League Intelligence at the time requested the station and system for Intelligence use. This was approved and the system was subsequently deleted from most charts and the approach algorithm became a tightly held secret. Frequently, a posting to Anchorage Station is a long term posting, if not a lifetime posting.
Once the system was fully under Intelligence's purview, it became a blacksite and storage for dangerous or unexplained objects found in League and allied space. These objects are examined and researched to determine what, if anything, affected them. 4 out of 5 times, the answer has been "subspace is weird" though this is almost always an unsatisfying answer.
Each Director has had their own side projects and obessions. Frequently, the Anchorage is used to facilitate those projects and obsessions. Much like the Republic Intelligence Directors have their bunker under the Tjoritja National Park in Australia, the Anchorage is part refuge, part museum, and part personal workshop.
Director McKenzie has been one of the least hands-on Directors when it comes to the Anchorage, perferring to use it as an extremely secure quarantine site for ships suffering curious fates. When a ship is taken to the Anchorage, his directive to the staff and crew is to figure out the issue, regardless of cost or time.
LSS Meshach - Moved to the Anchorage after a rampant systems failure following the Revelation-class refit. Currently, engineers are attempting to discover exactly what happened to the systems and how.
Diocese of Demeter - A passenger liner launched in the early 2400's. On a routine repositioning trip between Calysto and New Corinth, the Diocese dipped into subspace just beyond the orbit of Calysto's moon and almost immediately surfaced again completely without power. Calysto System Patrol investigated and found the entire crew and passenger compliment dead and mostly decomposed. Further investigation revealed that the internal systems had logged nearly 80 years passing between their initial dive and their surfacing.
The CNK Director's Ship
The Voyager 1 Probe
TRS Marianas - An early Terran research ship dating back to the century after Second Contact.
The Subspace Observatory - Originally planned as a means to better chart subspace, the Observatory produced some almost universally upsetting results and was quickly snatched up by League Intelligence, nominally to aid in Project Farscape.