I am working currently on a small-scale map using among other sources Natural Earth shapefiles (NE).
For an unknown reason, one of the polygons created by me on the basis of the fragments of NE coastline and administrative border can not be selected with Select tool and merged with other features. It can be selected through the Attribute Table but after merging it disappears completely (instead of being added to other territories of Dutch East India [the map depicts the 1905 situation]).
I checked validity of both lines that were used to create the polygon and the polygon itself. The validator does not show any errors, neither there are any error messages in the log windows (as it was the case in Cannot select polygon using QGIS). I suspect something may be wrong with the polygon but I cannot figure out what exactly is wrong. The shapefiles in question are temporarily uploaded to GitHub. I do not use spatial index, the set of shapefiles contains only the following files: .cpg, .dbf, .prj, .qpj, .shp, and .shx
Using QGIS 3.4.2-Madeira under Ubuntu 16.04
Best Answer
After check that the polygon is not closed correctly, you can fix it using the editing options.
Menu bar > Layer > Toggle Editing.
Digitizing Toolbar > Vertex Tool.
Click right on map to open Vertex editor panel.
The first and the last points of a valid polygon must be the same point. If they are different, the ring is not closed and the polygon cannot be built correctly. If you select the first vertex (0) and the last vertex you can see that are not the same point.
Vertex 0
Vertex 1981
You only need to move one of them to the same position than the other and save the changes.
Now you can select correctly the polygon because is closed.