Managing one's digital footprint is overwhelming, as it spans multiple platforms and involves countless context-dependent decisions. Recent advances in agentic AI offer ways forward by enabling holistic, contextual privacy-enhancing solutions. Building on this potential, we adopted a ''human-as-the-unit'' perspective and investigated users' cross-context privacy challenges through 12 semi-structured interviews. Results reveal that people rely on ad hoc manual strategies while lacking comprehensive privacy controls, highlighting nine privacy-management challenges across applications, temporal contexts, and relationships. To explore solutions, we generated nine AI agent concepts and evaluated them via a speed-dating survey with 116 US participants. The three highest-ranked concepts were all post-sharing management tools with half or full agent autonomy, with users expressing greater trust in AI accuracy than in their own efforts. Our findings highlight a promising design space where users see AI agents bridging the fragments in privacy management, particularly through automated, comprehensive post-sharing remediation of users' digital footprints.