Depending on the humidity in the area where you live, strings will sooner or later become tarnished. That is the very first stage of corrosion, but it will take many, many years for strings to rust beyond hope.
Brighten dull strings by rubbing them with a small wad of fine steel wool. Then, take a small rag barely wetted in silicone lubricant and coat the strings with an imperceptible protective coat. Don't allow the lubricant to run down the tuning pins because it will loosen them and make tuning difficult. Keep in mind that the biggest enemy of strings is the acids from hand grease and sweat. If you tend to touch your strings a lot, get in the habit of wiping them after use.
Dulcimer strings hardly ever break from normal use. Sometimes, when tuning, a player may be plucking one string and tightening another one until it breaks. Duh.