[D] How KV cache is valid in LLM transformer

Seeing a lot of literature mentioning using KV cache for transformer models to reduce compute in decoder, but in my understanding, when the sequence reaches maximum context length and each left shift renders the left-most token out of scope, the KV cache would lose validity, apparently because a previously participating token vanishes, is that correct?

cache compute context decoder literature llm machinelearning reduce shift token transformer transformer models understanding