Grown software systems often contain code that is not necessary anymore. Unnecessary code wastes resources during development and maintenance, for example, when preparing code for migration or certification. Running a profiler may reveal code that is not used in production, but it is often time-consuming to obtain representative data this way. We investigate to what extent a static analysis approach which is based on code stability and code centrality, is able to identify unnecessary code and whether its recommendations are relevant in practice. To study the feasibility and usefulness of our static approach, we conducted a study involving 14 open-source and closed-source software systems. As there is no perfect oracle for unnecessary code, we compared recommendations of our approach with historical cleanup actions, runtime usage data, and feedback from 25 developers of 5 software projects. Our study shows that recommendations generated from stability and centrality information point to unnecessary code. Our results suggest that static analysis can provide quick feedback on unnecessary code that is useful in practice.