Does corrosion follow the law of conservation of mass? For e.g .Due to rusting , iron becomes weak .So it should become weak only if the amount of iron is reduced. Even if we say the reduced iron is now the rust ,the amount of rust practically is very less comparing to iron.
The answer to the question in the title is yes. 

Iron oxide flakes away from the iron so just looking at the iron would make you think that the mass has disappeared; it's actually on the surface below, unless someone has moved it.