Equipping Large Language Models (LLMs) with persistent memory enhances interaction continuity and personalization but introduces new safety risks. Specifically, contaminated or biased memory accumulation can trigger abnormal agent behaviors. Existing evaluation methods have not yet established a standardized framework for measuring memory misevolution. This phenomenon refers to the gradual behavioral drift resulting from repeated exposure to misleading information. To address this gap, we introduce MemEvoBench, the first benchmark evaluating long-horizon memory safety in LLM agents against adversarial memory injection, noisy tool outputs, and biased feedback. The framework consists of QA-style tasks across 7 domains and 36 risk types, complemented by workflow-style tasks adapted from 20 Agent-SafetyBench environments with noisy tool returns. Both settings employ mixed benign and misleading memory pools within multi-round interactions to simulate memory evolution. Experiments on representative models reveal substantial safety degradation under biased memory updates. Our analysis suggests that memory evolution is a significant contributor to these failures. Furthermore, static prompt-based defenses prove insufficient, underscoring the urgency of securing memory evolution in LLM agents.