Modern LLM workflows, such as retrieval-augmented generation (RAG) and LLM agents, build long prompts from multiple independent text segments, making prefill a major source of computation. Reusing KV caches is therefore important for reducing serving costs and latency: distributed caching systems spread KV cache across a cluster to increase aggregate capacity, while position-independent caching (PIC) enables reuse of recurring segments under different prefixes. However, existing systems distribute KV caches but still rely on prefix caching (PC), while existing PIC methods enable position-independent reuse without cluster-wide resource management. We present Nebula, the first distributed LLM serving framework to treat PIC segments as first-class citizens, enabling remote PIC reuse and parallel prefill. To track PIC's fine-grained, asynchronous state changes, Nebula combines optimistic accounting with event-driven updates to provide a timely and truthful cluster view for cache management and prefill scheduling. To accommodate diverse reuse patterns across workloads, Nebula leverages cluster-wide ghost-hit feedback to automatically tune the allocation of shared cache capacity between PC and PIC. Finally, Nebula incorporates queueing, computation, and KV transfer costs into a unified prefill completion time model to guide elastic parallelism adjustment and locality-aware compute placement. Across four models and four real-world RAG and agentic workloads, Nebula reduces median TTFT by an average of 61.4% compared with the strongest existing baseline and recovers an average of 76.1% of the tokens missed by prefix caching.

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