The first step in these cases is to understand/access the situation and condition of the effected parts. Which we can't do long distance. But I've seen, perhaps hundreds, of similar problems over the years and i'll lend my speculation and advice.

I suspect that the rear hub bearings are contained in a retaining ring, the ball count is less the would be so if there were all the balls that would fit within the bearing so a sheet metal ring with fingers that hold the fewer balls apart and in their evenly spaced apart locations during normal operation. For what ever reasons this retaining ring has become damaged and the balls now will move around and the axle will no longer be contained in the center of it's intended rotation (or actually the hub's rotation about the stationary axle). When this happens the wobbliness will cause the sheet metal dust cap to become distorted and come loose from it's fittings. I believe this is what we see around the axle just outside of the cogs. the other failure mode is the hub's bearing cup (the curved surface that the balls roll within) can fracture and collapse. The resulting is much the same as the retaining ring's failure.

These things don't happen in an instant. It takes time and repeated cycles (pun) of use (as in miles of use) for steel to distort, crack, bend, wear and otherwise fail in it's designed function. That you only felt the problem at the point that the wheel's function dramatic change says that you didn't take care to maintain and monitor your bike well enough o off set the pending in time to avoid the problem. In this case ignorance isn't bliss.

So one might take apart the hub by first removing the cog set from the hub then the axle from the hub. Both require bike specific tools and some basic mechanical skill. Then the parts can be all cleaned off and examined for condition. In the dream world the damaged parts could be replaced and all reassembled to go on for many more miles of use. In reality you'll likely discover that the rolling surfaces, the axle mounted cones, the hub shell cups, the dust cap, the balls and maybe the axle are damaged. depending on the local shops you have access to some of these might be sourced but the hub shell cups not so. They are a pressed in and not replaceable part.

So you'll likely decide to replace the wheel as a whole and transfer the cog set, rubber, reflector and readjust the gears and brake to suit. As a replacement wheel might cost $30-45 and if done by a shop the labor will be less then the tool and educational costs. We would estimate around $ 55-70 total if brought in to our shop. Many times the rider thinks about the value of the bike and might decide to get another bargain basement big box. Others feel that a known bike is worth it.

This situation speaks to how the bike was assembled and maintained after purchase. The rest of the bike is now well used and might suffer from the same lacking assemble and maintenance. But a new bike bought in the same way is also likely to suffer from the same assembly concerns. The future is yours to pick. Andy.