The Typhon Sector takes it name from the fact that almost the entire sector is inside the Typhon Expanse. All that is except for one small corner about 245,163 km by 84,826 km by 4,472 km. For a very long time this region was the edge of not only the Federation but of explored space. This did not last and the Federation has now established an Embassy at Duronis II on the other side of the expanse from the Federation.
Following the destruction of Ivor by a Borg cube in 2373, a special Starfleet taskforce rendezvoused in the Typhon Sector. They selected this location due to the unusual properties of the Typhon Expanse. It allowed them to ambush the Borg cube as it skimmed along the edge of the expanse. The initial contact was in the small corner of the sector not inside the Typhone Expanse.
This force was commanded by Admiral Hayes, however they were unsuccessful in hindering the Borg Cube's advance, despite fighting it all the way to Sector 001. The cube was eventually defeated as the Enterprise-E joined the fleet with a solution.