The addition of Terriers would complement another Players Burrows suggestion to make that mechanic more involved.
Specifically for Fox the Wire Fox Terriers and Smooth Fox Terriers; They are dog breeds that are known for clearing fox holes. They were originally bred for fox hunting in England.
Or Jack Russells for a broader scope of burrowing animals (all terriers could theoretically be used for clearing burrows) they are first and foremost a working terrier. Originally bred to bolt foxes from their dens during hunts, they are used on numerous ground-dwelling quarry such as groundhog, badger, otter, and red and grey fox.