I know it is an oxymoron (btw, I already asked what the best term for it is, in the first post) and, therefore, your question sounds like asking to describe a hole. A hole is usually described by describing what is missing, no the hole itself. Which may or may not be the right thing to do.
I would say that, based on the experience on OSM (Weglose 'Wege' im Hochschwab), a path is a way that is clearly visible on the ground, or is known to a (particular?) group of people, is found elsewhere on the maps, or whatever other arbitrary reason one may have. A “pathless path” is a way that does not fall into those categories, yet serves exactly the same purpose. Hence the need for a proper way. In the legend from a paper map, posted by Hungerburg, it would perhaps best be described by Traces.
Truly “Weglose Gelände”, or pathless areas, likely do not need a line.
The lack of visible path is caused by the characteristics of the terrain (rock or hard mountain grass) and the (small) number of people who pass through it, possibly choosing a way that is close by, such as walking across a grass field. However, just adding a “pathless path” across the field shows that there is a route there. And it is not just a relation linking a starting and ending point, because it shows that one should follow a certain trajectory, since going a different way would be way more difficult and dangerous, as described in Alpinist routes marked as footpaths.
It would describe areas and ways such as Weglose 'Wege' im Hochschwab - #16 by _MisterY
And one possible purpose would be to find ways through Weglose 'Wege' im Hochschwab - #13 by _MisterY.
Edit: The purpose is two-fold. 1) To make it clear to people who expect to find a path there, that there is no such thing. 2) To make it clear to people who expect to find dangerous terrain there, that there is a possible way through.