You're a little inexperienced with terminology so I may be understanding you wrong, but I think your hub is a cup and cone style with loose ball bearings captured between the hub cups and the axle cone. In these systems, the cups are nearly never replaceable. The cones are, and are more often significantly worn, although getting a matching replacement can be a significant challenge. A well maintained bicycle has the bearings replaced and the hub cleaned and regreased on a semiregular basis and can enjoy very long service life in such cases, but in a hub that was always adjusted too tight and then run into the ground you can ruin the wheel in just a couple seasons. In the majority of cases, rebuilding the wheel with a new hub is not cost effective. I like this kind of bearing arrangement because the tools to service them are ubiquitous, and the bearings are readily available and cheap. In other hubs, the bearings are cartridge units. These are typically replaced rather than serviced per se, and have the advantage that the inner and outer races are replaced with the bearing cartridge.
The best you can do besides replacement is probably replace the bearings and cone and make do as best as possible. The cones are really hard to find a correct replacement for--it needs to match the shape of the old cones and the axle diameter and thread pitch.
https://wheelsmfg.com/products/hub-p...cones.html?p=1 is probably the easiest source for cones. Most bike shops will pull them off dead hubs and have a drawer, possibly augmented by a few tackle boxes of new cones, and will try to match as best they can.