Execution-aware LLM agents offer a promising paradigm for learning from tool feedback, but such feedback can be expensive and slow to obtain, making online reinforcement learning (RL) less practical in certain scenarios. High-coverage hardware verification exemplifies this challenge due to its reliance on industrial simulators and non-differentiable execution signals. We propose LLM4Cov, an offline agent-learning framework that models verification as single-step state transitions guided by deterministic evaluators. Building on this formulation, we introduce execution-validated data curation, policy-aware agentic data synthesis, and worst-state-prioritized sampling to enable scalable learning under execution constraints. We further curate a reality-aligned benchmark adapted from an existing verification suite through a revised evaluation protocol. Using the proposed pipeline, a compact 4B-parameter model achieves 69.2% pass rate and 90.4% average coverage in CVDP-ECov under agentic evaluation, outperforming its teacher by 5.3% and 10.5%, demonstrating competitive performance against models an order of magnitude larger.