The owner of that car must never do any kind of periodic checking. Like.... that's pretty dry. I could see the oil being LOW with an improperly installed half shaft.... but, to be completely empty??
I've had leaky diffs on a lot of my junk but none of them ever ran dry and we're talking old school diffs where the cover is the oil seal and is below the level of oil.

This thing would've been SPEWING oil at a noticeable rate. Or, more likely.... the shop that did the axle work.... if they did the axle improperly.... did they maybe drain the diff and forget to refill it?