In The Simpsons Movie, the town of Springfield is covered in a giant impenetrable dome, leaving the people trapped inside.
There is a scene showing various characters trying to break through (including Drederick Tatum trying to punch through it!) But no one ever suggests simply digging under, even after OFF escape through a strange type of sink-hole in full view of the public!
I like to think that this is a deliberate joke by the writers - i.e. the Springfieldianites are simply not smart enough to come up with that idea, but was there a reason ever given?