How can we show the boundary of a WordCloud shape?

Question

WordCloud can arrange the words inside a shape.

data = EntityValue[CountryData[], {"Name", "Population"}];
WordCloud[data, Disk[], WordOrientation -> "Random", Frame -> True]

As you can see from the plot range, the coordinates in the final word cloud don't seem to be related to the coordinates in the original shape specification. This is true regardless of whether the shape is specified as an image, graphics or region.

I would like to show the word cloud together the original shape. E.g. something like this (manually positioned):

I need to do this not for a disk/circle but any complex arbitrary shape. How can I achieve this? Is there any way to retrieve the mapping between the coordinates of the original shape and resulting word cloud?

Here's a random complex shape to test on: CountryData["Ethiopia", "Shape"].

Answer 1

shape = CountryData["Ethiopia", "Shape"]; 
mask =  ColorNegate@Binarize[shape, .99];

data = EntityValue[CountryData[], {"Name", "Population"}];
wc = WordCloud[data, mask, WordOrientation -> "Random", Frame -> False];

shapeRange = PlotRange /. AbsoluteOptions[shape, PlotRange];
cloudRange = PlotRange /. AbsoluteOptions[wc, PlotRange];

tr = FindGeometricTransform[cloudRange\[Transpose], shapeRange\[Transpose]][[2]];

Show[
 wc,
 Graphics[
  {
   EdgeForm[Black], FaceForm[],
   GeometricTransformation[shape[[1, 3]], tr]
   }
  ]
 ]

Since gpap reported problems with Italy here's Italy. I increased the image size of the bitmapped mask a bit to catch more of the complex coastal shape using:

shape = CountryData["Italy", "Shape"];
mask = ColorNegate@Binarize[Image[shape, ImageSize -> 1000], .99];