It won't come out, the axle runs through it. If it keeps slipping out either the bearings are shot or there was insufficient pre-load during set up. You definitely do not want it slipping out. I would have someone experienced with differentials look at it.
Looking at photos I took when I first cracked open my diff covers (shortly after I bought it) it appears that damned shim was always loose. I suppose that I was always too concentrated on the ring gears and carrier to notice.
I don't know exactly how the rust started to develop nor the source of the sludge, but here is what I know:
My ~8 o'clock
diff cover bolt was loose - not even finger tight.
The
breather hose was in questionable shape, not sure how it went to hell in a couple of months like it did, but I'm replacing it this evening with a new one. I'm also not sure where the end of that thing actually pops out - it disappears up near the top of my fuel tank somewhere, so it's
possible stuff got in through the end.
I have no idea what the condition of my axle seals are, I don't see any oil coming out anywhere. I'm a few weeks away from getting new Revolution rear axles anyway, and I just got the tools that I need to replace them.
Beyomd that, I'm planning on swapping out my front and rear axle pinion yokes (793's) with 1310's to match up both my front 1310 DS yoke and rear 1310 CV yoke, because right now I have to use Frankenstein u-joints.
Since I'm taking care of those driveline issues once and for all, I am now seriously considering a re-build of (at least) my rear diff soon. I don't like not trust any shops in my area and I'm a fast + motivated learner. I need to be able to service my diffs on my own anyhow, so now would be just as good of a time to learn as any.