Using the magic of DATABASE, I've took it upon myself to analysis my excel information to determine what triggers this encounter which in turn closes the Sleeping Fangs encounter. As it is late at night, and I'm only just now getting my toes wet with the magic of DATABASE, I've done nothing fancy that nobody couldn't do using just excel. I simply created a table and ran a query. Here are my results.
Of the 19 runs I've processed, the fewest number of Fangers I've killed before encountering this encounter is 10. 5 out of my 19 runs this result happened. There does not seem to make a difference if you kill gang enforcers or dockside gangers. In one of my runs, I killed 5 gang enforcers and 5 dockside gangers before encountering the Empty House.
Also of note, despite the extra attention you would expect burning a house full of sleeping fangers would create, it also seems to make no difference on whether this encounter is open for, erm, encountering. I noted in 2 of my runs, I burned a house full of sleeping Fangers upping my total kills to 9. The very next encounter I got was another group of of sleeping Fangers, whom I burned, bringing my total to 13.
I also heavily suspect that the zone of the Sewer Hideout you kill the Fangers also make no difference. I haven't yet, however, designed my database to analyze that.
So, it is almost conclusive to my mind the the encounter conditions for this encounter is to kill at least 10 Fangers.