LiHo_xY_1−xF₄ is an insulator where the magnetic Ho³⁺ ions have an Ising character and interact mainly through magnetic dipolar fields. We used the muon spin relaxation technique to study the nature of its ground state for samples with x ≤ 0.25. In contrast with some previous works, we did not find canonical spin glass behavior down to ≈15  mK. Instead, below ≈300  mK we observed temperature-independent dynamic magnetism characterized by a single correlation time. The 300 mK energy scale corresponds to the Ho³⁺ hyperfine interaction strength, suggesting that this interaction may be involved in the dynamic behavior of the system.