Carbon steel is iron containing some carbon in various forms of iron carbide.
When it rusts (oxidises), the iron becomes part of all kinds of crystalline and amorphous iron oxides and hydroxides, mostly as Fe3+.
Where does the carbon go in this process? Does it also oxidise to carbon dioxide or monoxide and leaves the system as a gas? Does it combine with the iron to form siderite (iron carbonate)? Does it remain as graphite or some other form of elemental carbon? Something else?