State-disaggregated Network Function Virtualization (NFV) architectures decouple NF states from packet processing logic to achieve elasticity and resilience in stateful NFs. However, the existing state disaggregation approaches suffer from either poor NF performance due to frequent remote state access or potential inconsistencies in state updates when multiple NF instances concurrently access shared states. Moreover, they do not properly support state rejuvenation/expiration which is required for resource scalability of stateful NF operations. This paper presents a new state-disaggregated NFV system called RESCue that addresses these problems. RESCue handles remote state access differently for shared and private states. For efficient and consistent access of shared states, it leverages a lightweight custom control message protocol between NFs and a centralized state server. For private state access, it adopts a remote-paging- based interface to avoid introducing expensive blocking remote access within the critical path of NF packet processing. Finally, it utilizes non-blocking operations for state rejuvenation/expiration handling to minimize its performance overhead. Our evaluation of a RESCue prototype shows that it can handle NF scaling and failure recovery well, while supporting consistent state updates and state rejuvenation/expiration without compromising performance.