Make navmesh agent follow terrain

Hi! I have large terrain mesh, and I want navmesh agent to follow it properly. No matter what setting I choice for navmesh generation, it is not covering the whole terrain surface properly. I.e. there are places, where character simply falls below the surface.

The easy solution would be to add rigidbody, freeze anything but "y", and make it stick to the terrain this way. But navmesh agent for some reason overwrites rigidbody.

Do I have any other option here?