We report a persistent low-energy phonon broadening around qB∼0.28 reciprocal lattice unit (r.l.u.) along the Cu-O bond direction in the high-Tc cuprate Bi2Sr2CaCu2O8+δ (Bi-2212). We show that such broadening exists both inside and outside the conventional charge-density wave (CDW) phase, via temperature-dependent measurements in both underdoped and heavily overdoped samples. Combining inelastic hard x-ray scattering, diffuse scattering, angle-resolved photoemission spectroscopy, and resonant soft x-ray scattering at the Cu L3-edge, we exclude the presence of a CDW in the heavily overdoped Bi-2212 similar to that observed in the underdoped systems. Finally, we discuss the origin of such anisotropic low-energy phonon broadening and its potential precursory role to the CDW phase in the underdoped region.