Deadhouse Gates, on Ch 20, said:
It sat unmoving for a few more minutes, idly plucking at its own tail, then swung about and scampered into the hallway, coming to a stop before the suit of armour.
The massive, closed great helm tilted with a soft creak, and a ragged voice came from it. 'I am pleased my solitude is at an end, little one. Tremorlor welcomes you with all its heart... even if you have made a mess on the hallway floor.'
Later, when Fiddler, Apsalar, Crokus et al arrive in the Deadhouse, they walk past a suit of armour:
Deadhouse Gates, on CH 23, said:
The group paused to regard it briefly, in silence, before continuing on to the opened doors.
So it looks like each Azath house has a suit of armor as its "Guardian"... lets call this the Battle Guardian, since a suit of armor can obviously not serve tea and cakes!
Moby's role is also that of a guardian, but I would call it the Butler Guardian. This is also the role that Raest seems to be fulfilling in Finnest House and a Jaghut (Jhenna?) was fulfilling in the Deadhouse before she got taken out on the night of knives. We may assume Gothos fills this role for the Deadhouse - the Azath seem to prefer Jaghut for this role, but in the case of Tremorlor settled for a bhok'aral...
Besides the Battle Guardian and the Butler Guardian, the Deadhouse has one or two Watchmen Guardians as well, who don't reside in the Azath, but who keep a handle on things in their vicinity. These were the two people (I forget their names) who handed over their role to Temper. This may well be an exceptional case since Malaz City has such a happening nightlife.
So yeah, its raining guardians... Battle, Butler, Watchmen