Samm,
In this case common sense doesn't work...
FCAW filler metals, both gas and self shielded, can be sensitive to exposure. The time they can be exposed, and the effects of exposure, are dependent on the product and the environment. If you're doing code critical work, the wire needs to be removed from the feeder and wrapped up at the end of the shift. Even overnight exposure in a heated or airconditioned shop can affect some products; let alone storage outside...
Some users will store partially used spools in a conditioned space when not in use. Others just throw away partially used spools and start with fresh wire every shift. To them, it's just not worth the risk. Some manufacturers vacuum pack their spools to preserve the wire during warehouse storage. Others used sealed buckets/containers to keep moisture out.
For the hobbyist, doing non-critical work, FCAW fillers could be left out. They may run rougher, and produce more spatter than fresh filler metal; right from the package. That said, I've seen lightly rusted wire sometimes weld just fine. It just depends on the product. But I wouldn't use wire left out more than a day for anything that needs to meet a high standard of quality.
I'm not aware of any manufacturer that recommends baking wire, as you might with stick electrodes to 'recondition' the filler metal after exposure. But it might be worth checking their websites for recommendations before you through out a large spool. Or call their customer service people and see if they'll give advice on how to recondition a spool.
FCAW filler metals are made by one of two methods. The sheath is formed by either drawing a rod of metal into a U shape, filling with flux, and formed to close into a tube. Or the sheath starts as a thin strip of steel, which is formed into a tube and simultaneously filled with flux. Either way, there's a seam in the tube that is not hermeticly sealed. So moisture is easily absorbed into the wire. All fluxes are prone to absorbing moisture, either because of the ingredients or simply because they're made of powders with very high surface area.