Long-context inference is central to modern large language model (LLM) applications such as retrieval-augmented generation and multi-document reasoning. To mitigate the growing inference cost, recent work has explored key-value (KV) cache reuse to reduce redundant prefill computation. However, existing reuse methods primarily focus on computation savings and overlook a critical bottleneck in long-context LLM serving: the cost of storing and accessing large KV caches. While KV compression appears to be a natural complement, naively combining compression with non-prefix KV reuse often leads to severe accuracy degradation. In this work, we propose C
2KV, a unified framework for non-prefix KV reuse that jointly optimizes KV extraction and inference-time concatenation. C
2KV learns a composable and compressed KV cache manifold that is explicitly designed to be position-agnostic. Our approach introduces a lightweight sidecar Extractor with learnable compression tokens and a structured attention flow, enabling modular KV representations that can be flexibly reused and concatenated without modifying the frozen base model. We further employ a compression-concatenation co-training strategy to align extraction-time representations with their downstream reuse behavior. Extensive experiments across multiple long-context benchmarks and model families demonstrate that C
2KV significantly reduces KV cache storage and transfer costs, achieving up to 17
× inference speedup under long contexts, while preserving generation quality.