Yes, voles or field mice will kill hosta plants if they eat the roots and then push the damaged plant out of the soil. You can save the plant by shoving it back into the hole and firming soil back around any remaining roots. The voles are easy to catch with a mouse trap set near the openings to their runways (look for small holes in the ground)  either a traditional mouse trap or the live catch type. Peanut butter is a good bait. Voles and mice use mole runways to feed on roots but moles feed mostly on earthworms and grubs so do less damage to plant roots then voles. If you do trap a mole you should make sure it is dead then bury him in his own runway. This will discourage the voles from using that runway as their underground highway.  Hostas are tough perennials so don't despair. Keep growing, Marianne Binetti