Context: Coping with rapid requirements change is crucial for staying competitive in the software business. Frequently changing customer needs and fierce competition are typical drivers of rapid requirements evolution resulting in requirements obsolescence even before project completion. Objective: Although the obsolete requirements phenomenon and the implications of not addressing them are known, there is a lack of empirical research dedicated to understanding the nature of obsolete software requirements and their role in requirements management. Method: In this paper, we report results from an empirical investigation with 219 respondents aimed at investigating the phenomenon of obsolete software requirements. Results: Our results contain, but are not limited to, defining the phenomenon of obsolete software requirements, investigating how they are handled in industry today and their potential impact. Conclusion: We conclude that obsolete software requirements constitute a significant challenge for companies developing software intensive products, in particular in large projects, and that companies rarely have processes for handling obsolete software requirements. Further, our results call for future research in creating automated methods for obsolete software requirements identification and management, methods that could enable efficient obsolete software requirements management in large projects.