The normals are reversed on the object for which the Clay Strip brush is currently not working. To prove this, try sculpting on the same object with any other brush. You will find that the new choice of brush will also not work. With the offending object selected,, go into Edit Mode, select all faces, and press Shift + n. Now your normals are pointing to the outside of your mesh instead of the inside. You should be able to sculpt on it now.

The normals are reversed on the object for which the Clay Strip brush is currently not working. To prove this, try sculpting on the same object with any other brush. You will find that the new choice of brush will also not work. With the offending object selected, go into Edit Mode, select all faces, and press Shift + n. Now your normals are pointing to the outside of your mesh instead of the inside. You should be able to sculpt on it now.