In general a Shadow Price equaling zero means that a change in the parameter representing the right-hand side of such constraint (in an interval that maintains the geometry of the problem) does not have an impact on the optimal value of the problem. Nevertheless, there are special cases like the Linear Programming problems that support infinite solutions (like the one described in this article) where a constraint with a shadow price of zero can be active in one of the optimal vertexes (the most common case is a constraint with a shadow price of zero that is not active in the optimal).