Pico:

You should know that copper rusts. It's just that the oxide that copper forms is very different than iron rust. Copper oxide remains well bonded to the parent metal (copper) and is fairly impermeable to both H20 and O2 molecules. So, the thicker the layer of brown copper oxide on copper, the better it protects the underlying parent metal from further oxidation. This is why copper water supply pipes in buildings will often outlast the buildings themselves.

Molten solder will bond well to bare copper, but not to copper oxide. So, the whole procedure of sanding the pipes and brushing out the fittings is to remove the copper oxide that has formed on the copper or brass since it was manufactured.

The primary purpose of soldering flux is to keep oxygen molecules away from the copper metal during the soldering process. The oxide film forms relatively slowly at room temperatures, but it's nearly instantaneous at soldering temperatures. The flux forms a physical barrier between the bare copper metal and the oxygen in the air while the joint is being heated, but at the soldering temperature, the flux is fluid enough to be displaced from the joint by the capillary pressure drawing the molten solder into the joint.

Now, a layer of solder over the copper will protect the copper from oxidation as well as flux will. So, if you take apart a soldered joint, you can wipe the solder off the pipe with a dry rag. But, there's no need to remove the old solder from the pipe or from the old fitting. You just treat the surface of the old solder as the new surface of the pipe.

In my opinion, it's best to flux the old solder just as you would a bare pipe or fitting. That's because flux contains a chemical called "zinc chloride". At soldering temperatures, zinc chloride becomes acidic and dissolves copper oxide much more readily than it dissolves copper metal. So, having plenty of flux in the joint is good insurance that there won't be any oxide in the joint to prevent the solder from bonding properly.

And, of course, just from the preceding, you should know to flux your pipes and fittings as soon after sanding or brushing them as possible. That way, there's the thinnest possible oxide film on the copper or brass to be dissolved by the zinc chloride, and therefore the best chance of leak-free solder joints. When people tell you to clean the old flux off the piping after soldering it's good advice because that old flux contains zinc chloride. It's just that at room temperatures, or even the temperature of a hot water supply pipe, the zinc chloride is very much less acidic, and would take forever and a day to do any harm to the piping.