Well, I always thought there wasn't such a thing as half a hole until the following happened:

A large hole mysteriously appeared in the middle of a main road in London's West End. The London Borough of Westminster sent workmen to fill it in, but they found out that the boundary with the City of Westminster ran through the middle of the road. They therefore proceeded to fill in only the half a hole that lay on their side of the boundary, leaving the other half a hole on the Westminster side unfilled.

So there is such a thing as half a hole; but I wholly believe they should have filled in the whole hole.