  Electron-phonon coupling, i.e., the scattering of lattice vibrations by
electrons and vice versa, is ubiquitous in solids and can lead to emergent
ground states such as superconductivity and charge-density wave order. Strong
coupling of phonons to electrons near the Fermi surface, which reduces the
phonon lifetimes and broadens the phonon peaks in scattering experiments, is
often associated with Fermi surface nesting. Here, we show that strong phonon
broadening can occur in the absence of both Fermi surface nesting and lattice
anharmonicity, if electron-phonon coupling is strongly enhanced for specific
values of electron-momentum, k. We use inelastic neutron scattering, soft x-ray
angle-resolved photoemission spectroscopy measurements and ab-initio lattice
dynamical and electronic band structure calculations to demonstrate this
scenario in the highly anisotropic tetragonal electron-phonon superconductor
YNi$_2$B$_2$C. This new scenario likely applies to a wide range of compounds.
