ill fill you all in later on when we actually start this thing (once i have everyones character sheet, and ive got all the prep work done [dont worry ive pretty much written the whole thing - its a good 100+ pages]) but for now, basically, the faction all got inolved in a large... war that ended in them being expelled from the Cage (thats Sigil) in a professional capacity.
in laymans terms this meant that while they no longer had the power to run businesses (like the Dustmen used to run the Mortuary), individual members could still work in those places, so using the above example, the Mortuary is now government-run, even though most workers are still dustmen (the faction itself fled to its main hideout in the negatvie energy plane)
so factions still have a presence in the cage, just not as organised or official. Two of te older factions (the Sign of One and the Beleivers of the Source) joined up into the Mind's eye after the war, while the Mercykillers split into the Sons of Mercy and the Sod Killers.
The war itself took pace some 5 years ago, not long before the rebirth or Orcus and any blood who calls the cage home will ahve lived through it (r left the city for its duration), so try to incorporate that into your histories if possible.