Yikes, honestly, masking is one of the worst features of the polargraph controller - such a kludge and not documented anywhere, I'm embarrassed.
Right, how it works: it's really meant to be used as a kind of "chroma key" mechanism for blanking out arbitrary shapes. I used it for making multi layered drawings like https://www.flickr.com/photos/euphy/6121848332/in/album-72157626497662024/. I made my background an unusual colour (#00FF00 is the default - bright green), and then use the "choose mask colour" button and click on any pixel in your picture that is that colour. Nothing appears to happen.
It's really difficult to see if you've got the right colour unless you use something really different to the rest of your image. There is a little information panel you can pop up with "ctrl+i" which has the masking colour at the bottom (calls it chroma-key colour), or you can set it manually in the default.properties.txt file with the controller.pixel.mask.color property.
If you've got your density preview on, then you can click around and you'll see some of the pixels disappear when they get masked out.
Sorry this is such a dog. Kong is right that you might be able to use the "brightest pixel" filter to get it to lift the pen over the white pixels too. Additional warning: This is implemented in a demented way too (if I remember rightly), but I think it does do the same kind of job. I think both approaches (masking or bright pixel filtering) will only lift over pixels at the ends of a row of pixels. I can't remember if there's a built-in way of lifting over blank/masked pixels inside a shape. What I mean is that you can lift over the pixels around the edge of your stag, but probably not the pixels inside your stag - even if they are masked/filtered.
That's a blast from the past, happy new year!