Will the Sagittarius A* Black Hole eventually swallow the entire Galaxy?
Black holes do not suck in matter any more than stars and planets do: an object in orbit would remain in stable orbit if nothing perturbed it.
However, in the long run ($10^{19}$ years and more) interactions between stars will perturb their orbits, making many of them end up in the central black hole. An easy way of seeing this is to consider a random close encounter between two stars. They will change velocities, and potentially one will get a sufficiently high velocity to escape the galaxy - but the other one, by energy conservation, would be more tightly bound and orbit in a closer orbit. Eventually the galaxy &quot;evaporates&quot; through this kind of interaction, with heavier stars congregating near and eventually into the black hole and the lighter stars mostly expelled. (For all the mathematical details of this and related processes, see Binney &amp; Tremaine's Galactic Dynamics).
Even if this did not happen, gravitational radiation makes a star orbiting something slowly lose angular momentum and spiral in, but this takes a far longer timescale.
Hence stars either fall in or are expelled over very long timescales.