Grass and lawn destruction
There are several types of wildlife that may dig in turf. Usually deer do not do this type of damage. Fox, skunk, moles, and/or raccoon may dig looking for soil insects such as earthworms, grubs, or other soil invertebrates. In the warmer months soil insects will be close to the soil surface and will be attractive to the wildlife. There is not much you can do to discourage them, other than reseeding. You can also try to tamp down the areas to see if the turf knits back together.
Soon soil insects will be burrowing lower in the soil profile and will not be an issue. Take a look at our website for photos http://extension.umd.edu/hgic/wildlife-lawns
Also, voles, a type of meadow mouse, feed on roots of trees and shrubs and make holes about the size of a silver dollar in beds and lawns. See photos https://extension.umd.edu/hgic/topics/voles
If this is not what you are noticing, you can send us photos.
Thank you for your prompt reply. I do see deer hooves' marks in the soil and had this last year as well. I will do as you suggested and treat for grubs and try to plant new seed. I think they are digging up one straw-like grass. I will consult with a landscaper for direction.