Usually that galaxy is moving over 4,000 miles per hour. With this photo evidence, we can now issue them a speeding ticket, we've got 'em dead to rights
At time 0 it emits a photon toward us. One year later, it's 1.1 light years farther away. The amount of newly-created distance between us is 0.9 light years. Some of that was created behind the photon, but I'll ignore that and just assume that all of the new space got in the photon's way.
Over that one year, the photon has traveled 1 light year towards us, and only 0.9 light years of that distance was new. So it's gotten closer to us by (a little more than) 0.1 light years. This rate will accelerate over time.
The object is still visible at the point where it emitted that photon, even though its velocity exceeds the speed of light.
I think it will ultimately become invisible, though.