Software automation has long been a central goal of software engineering, striving for software development that proceeds without human intervention. Recent efforts have leveraged Artificial Intelligence (AI) to advance software automation with notable progress. However, current AI functions primarily as assistants to human developers, leaving software development still dependent on explicit human intervention. This raises a fundamental question: Can AI move beyond its role as an assistant to become a core component of software, thereby enabling genuine software automation? To investigate this vision, we introduce AI-Driven Self-Evolving Software, a new form of software that evolves continuously through direct interaction with users. We demonstrate the feasibility of this idea with a lightweight prototype built on a multi-agent architecture that autonomously interprets user requirements, generates and validates code, and integrates new functionalities. Case studies across multiple representative scenarios show that the prototype can reliably construct and reuse functionality, providing early evidence that such software systems can scale to more sophisticated applications and pave the way toward truly automated software development. We make code and cases in this work publicly available at https://anonymous.4open.science/r/live-software.