If copper has started to corrode, can it stop? I've recently obtained a couple of electronics units which have suffered corrosion on their copper inductor coils. They were operated in conditions of intense humidity/heat and were placed near the sea. This has resulted in the complete failure in one of these units, where the inductor has come apart due to being eaten away by corrosion, and the other coil shows noticeable amounts of corrosion (patina present).

If I were to operate the latter device in a more forgiving environment (ie: putting a filter in front of it in an air conditioned room) will the copper continue to corrode regardless or will the oxide layer stop spreading further?
The previous answers doesn't take into account the environment: 


  They were operated in conditions of intense humidity/heat and were placed near the sea.


Near the sea means that there are certainly a lot of $\ce{Cl-}$ ions in your metal. Chloride ions are a very dangerous species for metals conservation they tends to depassivate the metal forming complex ions. In the case of copper occurs this series of reactions:
$$\ce{Cu^{+} + Cl^{-} &lt;=&gt; CuCl}$$

$$\ce{Cu^{+} + 2Cl^{-} &lt;=&gt; CuCl2- + Cl- &lt;=&gt; CuCl3^{2-} + Cl- &lt;=&gt;CuCl4^{3-} }$$

That lead to different copper corrosion product. (e.g. atacamite $\ce{Cu2(OH)3Cl}$, malachite $\ce{CuCO3.Cu(OH)2}$ (Did you see some blue-green pigment?), Cupric hydroxide $\ce{Cu(OH)2}$.

These are all dynamic equilibria so your copper with dry-wet, hot-cold cycle will continuously object of degradation until chloride ions are present.

Use distilled water with cotton to clean the salts deposit, dry quickly where you clean.  

Reference:


The Open Corrosion Journal, 2009, 2, 71-76
Corrosion Science 46 (2004) 109–135