Long-context decoding in Large Language Models (LLMs) is constrained by the cost of accessing and processing the Key-Value (KV) cache. Despite the evidence that attention outputs depend jointly on keys and values, most existing KV management methods rely on key-only pruning, as incorporating values incurs prohibitive additional overhead. In this paper, we propose Attention Run-time Termination (ART), a lightweight run-time mechanism that tracks accumulated attention outputs during kernel execution and terminates subsequent KV block accesses once further contributions become negligible. Rather than replacing KV selection, ART dynamically terminates redundant KV traversal on top of existing dense or sparse attention policies. We introduce a stability-based criterion that monitors both magnitude and directional changes of intermediate attention outputs, and provide a theoretical characterization of the resulting truncation error. Experiments on LongBench and RULER Needle-in-a-Haystack tasks show that ART increases the generation throughput of existing KV-cache methods by up to 20%, without compromising the quality of the results.