Last stable orbit, that's a good candidate.
There's two points that need to be conisdered:
The first is the question "At what point do the tidal forces across a stellar body exceed the ability of the stellar body to hold itself together gravitationally" - given the size of protostellar objects that we see, it seems unlikely that a new star will form if an already existing star can not hold itself together.
The second point is that the closest we have evidence for stars forming to a SMBH is within two light years of Sag A*.
I'd agree that ''the most stable orbit'' is required but sounds very vague because no one yet has defined the stable orbit. Though... it seems we can clear this up quite quickly.
I know of some experiments in which we have been able to ''see'' stars and other objects violently circling a supermassive black hole. I would wager, the stable orbits permit anything outside the immediate danger zone. The gravity is too strong to cause irregularities to form proper stars. Just outside this danger zone, similar perhaps to how we envision the Goldy Locks zone, is where all the cold activity is and where gas clouds might be altered by the surrounding gravitational field but not too much for it not to settle to some state in which the center of its gravity takes over.